The length of a rectangle is twice its width. If the perimeter is 36 ft find its area.
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calendarEducator since 2008
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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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calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
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.
To solve this problem, you will need to be familiar with the formulas for perimeter and area. Perimeter is adding all side lengths so for a rectangle you would add the 2 width's and 2 lengths. Area is length times width.
P=2l + 2w A= l(w)
The statement "length of a rectangle is twice its width" would be represented as follows:
length (l) = 2xwidth(w)
l = 2w
Because you know from the word problem that the perimeter is 36 ft you can substitute this into the formula for perimeter. You would also substitute the new equation for length into the formula in order to solve for the width with only one variable.
36=2(2w)+2w
Now you will solve the equation above by simplifying the right side of the equation by distributing the 2 outside of the parentheses inside by multiplying and then combine like terms.
36=4w+2w
36=6w
Next, solve for w by using inverse operations to isolate w. (divide both sides by 6)
w=6
Finally you will need to substitute the value for w (width) into the equation for length (l=2w) in order to determine the length and then calculate the area to answer the question in the word problem.
l=2(6)
l=12
A=l x w
A= 12 x 6
A= 72 sq ft
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
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