# The length of a rectangle is twice its width. If the perimeter is 36 ft find its area.

### 5 Answers | Add Yours

Let the length of the rectangle be L and the width be W.

Given that the length is twice the width, Then :

L = 2W .....(1)

But we know that the perimeter is 36.

==> 2L + 2W = 36

==> 2L + L = 36

==> 3L = 36

==> L = 36/3 = 12

==> W = 12/2 = 6

Now we will calculate the area:

==> A = L * W = 12* 6 = 72 square feet.

**Then the area of the rectangle is 72 square feet.**

Let the length of the rectangle be L. As the length is twice the width, the width can be denoted by L/2

The perimeter of the rectangle is 2*(length + width) = 2*(L + L/2) = 36

=> 2L + L = 36

=> 3L = 36

=> L = 12

width = 12/2 = 6

The area of a rectangle is length*width = 12*6

=> 72 square feet.

**The required area of the rectangle is 72 square feet.**

** WHAT WE KNOW**

*The length of a rectangle is twice its width. *

**l=2w**

*If the perimeter is 36 ft find its area.*

**P= 2 (l+w)=36**

**A=lxw=?**

Let's solve the find the length and width first. Using Perimeter equ first.

- Plug-in 2w for l: 2(2w+w)=36
- Combine like terms: 2(3w)=36
- Solve:
**w=6 ft** - Plug in the answer for w back into the equ to get l: 2(l+6)=36
- Distribute: 2l+12=36
- Subtract 12 from both sides: 2l=24
- Isolate variable by dividing 2 from both sides:
**l=12 ft**

Now that we know the length and the width, we can find the area

- A=lxw
- A=12 ft x 6 ft
- A= 72 `ft^(2)`

Use the equation 2L + L = 36 with L = the length

2L + L = 36 first combine 2L with L

By combing the like terms , you should have :

3L = 36 now divide both sides by 3 .

By dividing both sides by 3 , you should get :

L = 12 Which is the answer for the length

Now divide the length by 2 to get the width .

By dividing , you should get that the width equals 6 .

So now to find the area , multiply 12 with 6

By multiplying , you should get

= 72 which is your answer

Hi micahmorse.Here is your answer-

Let the width of the rectangle be x ft.

Then, its length= 2x ft

Now, Perimeter of a rectangle= 2(l+w)

This implies,

36=2(2x+x)

36=4x+2x

36=6x

so,

x=36/6

x=6 ft.

Hence, width=x=6 ft

length=2x=2*6=12 ft

Now,

Area= l*w

Area= 12*6

** Area= 72 square feet. ...Ans**