jmc

Question

A rectangle has integer side lengths. One pair of opposite sides is increased by 30% and the other pair of sides is decreased by 20%. The new side lengths are also integers. What is the smallest possible area, in square units, of the new rectangle?

Accepted Answer

Let a and b be the original side lengths. The new side lengths are 1.3a=13a/10 and 0.8b=4b/5. Therefore, the smallest possible integer values of a and b are a=10 and b=5. The new side lengths are 13 and 4, and the area of the new rectangle is 134=52 square units.