SOLUTION: One pair of opposite sides of a rectangle increases in length by 25%. By what percent must the other pair of sides decrease if the area of the rectangle remains the same?
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Question 1180102: One pair of opposite sides of a rectangle increases in length by 25%. By what percent must the other pair of sides decrease if the area of the rectangle remains the same? Answer by greenestamps(13203) (Show Source):
Work this kind of problem by thinking in terms of what FACTOR the one pair of sides is MULTIPLIED BY instead of in terms of percent increase or decrease.
An increase of 25% (i.e., 1/4) increases the measurement by a FACTOR of (1+1/4)=5/4. To keep the area the same, the other dimension of the rectangle must be changed by a factor of 4/5.
Original area: (x)(y) = xy
New area: ((5/4)x)((4/5)y) = xy
4/5 as a percentage is 80%, which means a decrease of 20%.
