SOLUTION: The perimeter of a rectangle is 72cm. If the length is increased by 20% and the width is decreased by 25% the perimeter remains the same . calculate the length and width of the o

Question 990404: The perimeter of a rectangle is 72cm. If the length is increased by 20% and the width is decreased by 25% the perimeter remains the same . calculate the length and width of the original rectangle
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!

w for width
L for length
20% increase is a factor, ;
25% decrease is a factor .

You will have two linear equations, which you can simplify, and then solve as a system for w and L.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

The perimeter of a rectangle is 72cm. If the length is increased by 20% and the width is decreased by 25% the perimeter remains the same . calculate the length and width of the original rectangle

Let original length and width be L, and W, respectively
Then: Perimeter = 2(L + W) --------> 2(L + W) = 72 ------- 2(L + W) = 2(36) ------> L + W = 36______W = 36 - L
Increasing length by 20% makes new length: 1.2L
Decreasing width by 25% makes new width: .75(36 - L), or 27 - .75L
We then get: 2(1.2L) + 2(27 - .75L) = 72
2.4L + 54 - 1.5L = 72
2.4L - 1.5L = 72 - 54
.9L = 18
L, or original length = , or cm
Original width: 36 - 20, or cm
RELATED QUESTIONS
The perimeter of a rectangle is 28cm. If the length were decreased by 2cm and the width... (answered by Tatiana_Stebko)
the length of a rectangle is 3times its worth. if the perimeter is 72cm. calculate the... (answered by macston)
The perimeter of a rectangle is 24 cms. If the length is increased by 4 and the width is... (answered by jkc52)
If the length of a rectangle is increased by 40% and its width is decreased by 20%, what... (answered by checkley77)
The perimeter of a rectangle is 68 cm. If the width is increased by 2cm. and twice th... (answered by mananth)
The perimeter of a rectangle is 68 cm. If the width is increased by 2cm. and twice th... (answered by mananth)
If the length and width of a rectangle is increased by 1meter then the area of a... (answered by ankor@dixie-net.com)
The length of a rectangle is 3 times the width. If the length is decreased by 4 m and the (answered by ankor@dixie-net.com,richwmiller)
The length of a rectangle is 3 times the width. If the length is decreased by 4 and width (answered by mananth)