SOLUTION: a rectangle has an area that is numerically twice its perimeter. if the length is twice the width, what are the dimensions?

Question 267515: a rectangle has an area that is numerically twice its perimeter. if the length is twice the width, what are the dimensions?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a rectangle has an area that is numerically twice its perimeter.
:
L*W = 2(2L+2W)
:
If the length is twice the width, what are the dimensions?
:
Replace L with 2W
(2W)*W = 2[2(2W) + 2W)]
2W^2 = 2(4W + 2W)
2W^2 = 2(6W)
;
divide both sides by 2
W^2 = 6W
W^2 - 6W = 0
:
factor out W
W(W - 6) = 0
:
Two solutions
W = 0, meaningless
and
W = 6 units is the width
then
2(6) = 12 units is the length
:
:
Is this true?
12*6 = 2(2(12) + 2(6))
72 = 2(24 + 12),
RELATED QUESTIONS
a rectangle has a length that is 3 meters longer than twice the width what are the... (answered by Fombitz)

A rectangle has a perimeter of 34 cm and an area of 52 cm2. Its length is 5 more than... (answered by lwsshak3)

Suppose that the width of a certain rectangle is 5 inches less than its length. The area... (answered by mananth)

Suppose that the width of a certain rectangle is 2 inches less than its length. The area... (answered by emargo19)

Suppose that the perimeter of a rectangle is 36 and the length is twice the width. What... (answered by benni1013)

The length of a rectangle is three more than twice its width. What are the dimensions of... (answered by swincher4391)

A rectangle is 5 feet longer than twice its width. If the rectangle has a perimeter of... (answered by jorel1380,chriswen)

The length of a rectangle is 6 inches less than twice the width. If the perimeter of the... (answered by ReadingBoosters)

The width of a rectangle is 15 less than twice its length. If the perimeter of the... (answered by MathLover1,josgarithmetic,MathTherapy)