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

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hala718's profile pic

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.

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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.

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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's profile pic

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 

= 72 which is your answer 

vanshsodhi's profile pic

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

Posted on

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

                       

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