The length of a rectangle is twice its width. If the perimeter is 36 ft find its area.
5 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
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
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
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
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 | Student, Grade 9 | (Level 1) eNoter
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