find area of triangle formed by (1,1) (2,3) (4 ,5) using heron's formula ​

Answers

Answer 1

Answer:

The area of a triangle is:

A = 1 unit²

Step-by-step explanation:

Given the points of a triangle

A(1, 1)

B(2, 3)

C(4, 5)

[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Distance between AB:

[tex]AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}[/tex]

     [tex]=\sqrt{1+4}[/tex]

     [tex]=\sqrt{5}[/tex]

so

[tex]a=\sqrt{5}[/tex]

Distance between BC:

[tex]BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}[/tex]

     [tex]=\sqrt{2^2+2^2}[/tex]

     [tex]=\sqrt{2^3}[/tex]

     [tex]=2\sqrt{2}[/tex]

so

[tex]b=2\sqrt{2}[/tex]

Distance between AC:

[tex]AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}[/tex]

    [tex]=\sqrt{3^2+4^2}[/tex]

   [tex]=\sqrt{5^2}[/tex]

    [tex]=5[/tex]

so

[tex]c=5[/tex]

Semiperimeter = sum of sides ÷ 2            

                       [tex]s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224[/tex]

Area of the triangle:

[tex]A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}[/tex]

[tex]a=\sqrt{5}[/tex][tex]b=2\sqrt{2}[/tex][tex]c=5[/tex]

[tex]A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}[/tex]

[tex]A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}[/tex]

[tex]A=1[/tex]

Therefore, the area of a triangle is:

A = 1 unit²

Related Questions

find the missing side lengths. leave ur answers as radicals

Answers

Answer:

m = 34 ; n = 17√3

Step-by-step explanation:

m = 17 × 2 = 34

n² = 34² - 17² = 867 = 17² × 3 ⇒ n = 17√3

Gina says that for all real numbers a and b, ab=ba. is this statement true or false? If false, give a counterexample

Answers

Answer:

True

Step-by-step explanation:

The communative property states that the order in addition and multiplication dosen't matter.

Evaluate the expression.
1.2 exponent 2
answer choices =
1.44
14.4
1.728
1.5

Answers

Answer:

1.44

Step-by-step explanation:

Answer:

the answer is 1.44

Step-by-step explanation:

Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.

                      Your welcome

Cara's new car holds 13.5 gallons of gas. If gas costs $2.98 per gallon, how much would it
cost her to fill the gas tank from empty?
Submit
O
Lenovo

Answers

Answer:

$40.23

Step-by-step explanation:

Answer:

40.23

Step-by-step explanation:

easy just do 13.5*2.98

Is m || n? Which theorem (which tool) did you use to decide?

Answers

Answer:

Yes. m is parallel to n. Since the 2 angles labelled are equal, by alternate angles rule, m is parallel to n.

Step-by-step explanation:

This is a question on angles. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Answer:

yes

Step-by-step explanation:

Yes m is parallel to n because the alternate interior angles are equal .

what is the correct evaluation of 3x-x+2,when x is equal to -4?

14

-6

6

-14​

Answers

-6 is the correct answer !


3(-4)-(-4)+2
-12+4+2
-8+2
-6

Answer:

(b) -6

Step-by-step explanation:

=3x-x+2

=3(-4)-(-4)+2

=-12+4+2

=-12+6

=-6

Factorise fully 2x+8

Answers

Answer:

2(x+4)

Step-by-step explanation:

To factor you have to divide both terms by the greatest common factor, which in this case is 2. Using distribution you can check your answer.

Answer: 2(x + 4)

Explanation: If you're asked to factor a polynomial,

the first thing you want to look for is the greatest common factor

for the terms that are involved.

The greatest common factor of 2x and 8 is 2.

So a 2 can factor out.

Inside the parenthses, we have each term divided by

the 2 that factored out of the polynomial.

So we have 2(x + 4).

Please help it would help a lot

Answers

Answer:

1/2

Step-by-step explanation:

Answer:

y÷x 1÷2=1/2 This is the answer.


You earned a 90% on a science test. You answered 18 questions
correctly. How many questions were on the test?

Answers

Answer:

20 questions

Step-by-step explanation:

10 divided by 20 is 0.9 which would be 90%

6 friends all use $2 off coupons to buy themselves movie tickets. They spend a total of $42 Write the equation

Answers

Answer:

(C / n) + 2

Step-by-step explanation:

Amount spent (C) = 42

Number of friends (n) = 6

Coupon on ticket = $2

Original price of ticket will be :

Cost per coupon ticket = (Total amount spent / number of friends)

(Total amount spent / number of friends) + coupon on ticket

= (C / n) + 2

= (42 /6) + 2

= 7 + 2

= 9

Ebony's bank balance first reached $400 on Day 4. The last day her balance was $400 was Day 8. Look at the picture. Brainliest Answer. Only answer if your 100% sure . ​

Answers

Answer:

It stays true because it stays the same amount so B would be the correct answer.

Step-by-step explanation:

Pam drivers 14,735 miles in one year. The next year she drivers 13,869 miles. How many miles did she Drive in all?

Answers

Answer:28604 in total

Step-by-step explanation:

just copy and paste hope this helps

Answer:

28604 miles

Step-by-step explanation:

Just add the two numbers to get the total number of miles:

  14735

+ 13869=

  28604

Austin made 5 quarts of his special from-scratch cupcake mix. He was able to make 32 identical cupcakes using 3.5 quarts of his special mix. Austin would like to bake 20 more identical cupcakes to ice each cupcake in the likeness of a playing-card. Does he have enough left to create 20 additional cupcakes? Explain.

Answers

9514 1404 393

Answer:

  no

Step-by-step explanation:

We can write a proportion to find how much mix is required to make 52 cupcakes.

  quarts/cupcakes = 3.5/32 = x/52

Multiplying by 52, we find ...

  x = 52(3.5/32) = 5.6875 . . . quarts needed for 52 cupcakes

This is more mix than Austin made. He does not have enough left for 20 more cupcakes.

A rectangle is 3/5 red. The rest is blue and yellow, but not in equal ratios. What could those ratios be? PLEASE HELP

Answers

Blue can be 1/10 and yellow can be 3/10 or other way around.

a window washer clean 38 windows in 2 hours at this rate how many windows did he clean in 7 hours?​

Answers

Answer:

133 windows

Step-by-step explanation:

2/3x = -36
Possible answers
+24
-24
+54
-54

Answers

Answer:

-54

Step-by-step explanation:

2/3x=-36

3*2/3=3(-26)

2x=-108

2x/2= -108/2

x=-54

PLEASE HELP ME WITH ME MATH In a survey of 3500 people who owned a certain type of​ car, 1750 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

50%

Step-by-step explanation:

3500 divided  by 1750 is 2 which is equal to 50%

What is the equation of the line that passes through the point (-5,-7)and has a slope of 2/5

Answers

Answer:

6.33333 is the answer <3

Multiply 1 4/5 * 1 ???

Answers

Answer:

9/5 or 1 4/5

Step-by-step explanation:

You’re welcome :)

Answer:

your answer will come to be 1.8

find the value of x and the measure of MNW

Answers

Answer:

VALUE OF X:

3x-13+61 = 90

3x+48 = 90

3x = 42

x = 14

MEASURE OF <MNQ:

3x-13

= 3(14)-13

= 42-13

= 29

A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases by 7/8 cup. On Day 2, the volume in the bowl decreases by 3/4 cup. What number represents the total change in the volume of water in the bowl after two days? Write your answer as a mixed number.

Answers

Answer:

-1 5/8

Step-by-step explanation:

Let the total amount in the bowl be x;

If on Day 1, the volume of water in the bowl decreases by 7/8 cup, the remaining water will be;

x - 7/8

If on day 2, the volume in the bowl decreases by 3/4 cup, the remaining volume of water after the second day will be;

= x - 7/8 - 3/4

= x - (7-2(3))/8

= x - (7+6)/8

= x - 13/8

This shows that the total change after the two days is -13/8

As a mixed fraction;

-13/8 = -1 5/8

1. An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.

Answers

Answer:

3 and 12

Step-by-step explanation:

3*5=15 and 15-3=12. The product of 3 and 12 is 36.

The integers are 3 and 12.

What is Algebra?

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

let the one integer be x.

Another integer = 5x - 3

According to question,

x *(5x-3 ) =36

5x ² -3 x =36

5x² -3 x - 36 = 0

5x² -15 x +12 x - 36 =0

5x( x-3) + 12 ( x -3) =0

(5x +12)( x- 3)=0

x= -12/5 or 3

So, the integers are 3 and 12.

Learn more about this concept here:

https://brainly.com/question/17023448

#SPJ2

Selena bought a TV for her bedroom. The original price was $299.99, but she bought it on sale for 30% off. Selena also paid 15% tax. How much money did she spend on the TV?

Answers

I believe $241.50 would be your answer

Substitute u = 26 into u + 34 to find the value of the left-hand side of the equation

Answers

Answer:

60

Step-by-step explanation:

The answer is 60 because the equation u = 26 tells us u is 26

So we can plug in 26 into u + 34

It should look like this 26 + 34 and it equals 60

pls mark brainliest

Name the theorem or postulate that lets you immediately conclude ∆ABD ≈ ∆CBD.
A. None of these
B.AAS
C.ASA
D.SAS

Answers

Answer:

The correct answer is B. AAS

Step-by-step explanation:

I took the test

hope this helps :)

SAS postulate is used to conclude that ∆ABD ≈ ∆CBD. Option D is correct.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

In the given triangle there are ACD, DB is the perpendicular bisector.

We need to prove ∆ABD ≈ ∆CBD.

In ∆ABD and ∆CBD

AB is congruent to BC by given diagram.

∠ABD ≅ ∠CBD both are 90 degrees.

BD ≅ BD both having common side.

∆ABD ≈ ∆CBD.

By SAS postulate.

Hence, the SAS postulate is used to conclude that ∆ABD ≈ ∆CBD.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ5

Helpoooooooooooooooooooo

Answers

Answer:

1. x >/= -1

2. x < 4

3. x </= -1

4. x >/= -2

5. x < -3

6. x </= 7

Step-by-step explanation:

write an equation of the line with a slope of -3/4 and y-intercept of -6

Answers

Answer:

y = -3/4x - 6

Step-by-step explanation:

Answer: y = (-3/4)x - 6

A bakery made 9 cakes using 3 bags of flour. The bakery uses the same relationship between cakes made and the amount of flour used to make all of their cakes. Which table of values shows the relationship between the number of cakes the bakery makes to the number of bags of flours the bakery uses?

Answers

Answer:

c = 3b

Step-by-step explanation:

9 cakes proportional to 3 bags of flower

cake = k(bag)

c = kb

9 = k(3)

k = 3

c = 3b

you didn't send any table of values but this is the relationship between the cakes and flour, you can use it.

please mark brainliest if you like the answer

How many numbers can be squared to get a value of 0?

Answers

Maybe zero? Not sure

Answer:

1

Step-by-step explanation:

0^2 equals 0 but 1 and -1 the numbers closest equal 1 so only one number can be squared to get 0



1. Adjacent angles are two angles in the same plane with a common

and a common

but no common interior points.

Answers

Answer:

Adjacent angles are two angles in the same plane with a common  VERTEX and a common  SIDE but no common interior points.

Step-by-step explanation:

Adjacent angles share a common side on the same vertes, but they do not overlap each other.

In the attached image, ∠ABD is adjacent to ∠DBC, but ∠ABC is not adjacent to any of them.

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