Question

Help!

Answer 1

A rectangle and a square have the same area. The perimeter of the rectangle is 240 meters and the width is a third of the length. Find the measurement of one of the side lengths of the square.

Answer 2

Assume L = Length of the rectangle and W = Width of the rectangle
L & W ate the two unknowns. We will need 2 equations to solve them.
The perimeter of a rectangle = 2(L + W) = 240
The problem says: the width is a third of the length ==> W = L/3

So we have two equations and you can solve for L & W.

Answer 3

So then what will the final equation be?

Answer 4

I can guide you to find the answer but I can't straightaway give you the answer.

Answer 5

oh okay. im fine with that

Answer 6

I derived two equations:
2(L + W) = 240 and W = L/3
You should be able to solve these two equations and find L & W.
Then you can find the area of the rectangle. Do these and I will tell you the next step.

Answer 7

I'm confused on what L/3 is. Does that mean to divide it or what?

Answer 8

Would it be 2L-6=240 ?

Answer 9

2L+6=240 I mean

Answer 10

@ranga

Answer 11

W = L / 3
Multiply bot sides by 3
3W = L

Put L = 3W in the first equation: 2(L + W) = 240
and you can solve for W first. What is W = ?

Answer 12

W=30. What do you mean by multiply 3 to both sides?

Answer 13

W = L / 3
We want to get rid of the 3 in the denominator so it would be easy to do the arithmetic.
In an equation you can multiply or divide both sides by the same number and the equation will remain unchanged.
Similarly you can add or subtract the same quantity from both sides abd the equation will remain unchanged.

Answer 14

Okay, and then to find the length will I need to multiply by 1/3?

Answer 15

L=90

Answer 16

No. W = 30.
L = 3W.
So you need to multiply W by 3 to get L.
L = ?

Answer 17

okay. L = 90 and W = 30. What is the area of the rectangle?

Answer 18

It'll be 2700

Answer 19

Correct. Now the area of this rectangle is the same as the area of another square.
Assume the length of one side of the square is x
What is the area of a square with side x?

Answer 20

Is it 675?

Answer 21

No. How did you get that?

Answer 22

I divided 2700 by 4

Answer 23

No. Assume the side of the square to be x.
Squares have all equal sides. So if one side is x, the area will be: x * x = x^2
Equate x^2 to 2700 and solve for x.

Answer 24

Is it 51.96? @ranga

Answer 25

Yes.

Answer 26

And thats the final answer?

Answer 27

How can I check my answer is right?

Answer 28

You can work backwards and see if the numbers agree.
Side of the square = 51.96. Its area = 51.96 * 51.96 = 2700.
We found L = 90 and W = 30 earlier for the rectangle. Its area = 90 * 30 = 2700 and so it agrees with the problem that the areas of the square and rectangle are the same.

L = 90 and W = 30 gives the perimeter as: 90 + 30 + 90 + 30 = 240 which also agrees with the perimeter of 240 given in the problem.

Answer 29

THANK YOU SO MUCH! I REALLY APPRECIATE IT!:)

Answer 30

Also, instead of giving the answer in decimal, they may give it as 30 * sqrt(3)
Don't worry. The value will be the same as 51.96 if you use your calculator. It is just a different way of saying the same thing.

Answer 31

You are welcome.

Answer 32

I'll stick with my answer being 51.96:)