The length of a rectangle is twice its width. If the perimeter is 36 ft find its area.
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.
If the perimeter is 36 ft find its area.
P= 2 (l+w)=36
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=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)
Hence, width=x=6 ft
Area= 72 square feet. ...Ans