SOLUTION: The width of a rectangle is decreased by 20%. By what percent would the length have to be increased for the area to remain the same?

Question 70119: The width of a rectangle is decreased by 20%. By what percent would the length have to be increased for the area to remain the same?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

The width of a rectangle is decreased by 20%.
By what percent would the length have to be increased. 
for the area to remain the same?

Let old width = W
Let old length = L
Old area = LW

Let p = the decimal representation of the desired percent 
increase in L. 

New width = W - .20W = 1.00W - .20W = .80W = .8W
New length = L + pL
New area = (L + pL)(.8W) = .8W(L + pL) = .8LW + .8pLW

New Area = Old Area

.8LW + .8pLW = LW

Divide every term by LW

   .8 + .8p = 1
        .8p = 1 - .8
        .8p = .2
          p = .2/.8
          p = .25 = 25%

Edwin

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