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

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

taangerine | Student, Grade 12 | (Level 1) Valedictorian

Posted on

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)`

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

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

vanshsodhi | Student, Grade 9 | (Level 1) eNoter

Posted on

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