   SEARCH HOME Math Central Quandaries & Queries  Question from Paul, a student: If the smaller dimension of a rectangle is increased by 3 feet and the larger dimension by 5 feet, one dimension becomes 3/5 of the other, and the area is increased by 135 square feet. find the original dimensions Hi Paul,

To solve this problem and the other two you sent us you need to read the question carefully and translate the English statements into mathematical equations. Consider this question.

If the smaller dimension of a rectangle is decreased by 2 feet and the larger dimension is increased by by 3 feet, one dimension becomes 6/5 of the other, and the area is increased by 250 square feet. find the original dimensions.

The length and width of the rectangle are the important dimensions so I am going to give them names. let the length of the rectangle be x feet and the width y feet, x > y. The area is then xy square feet.

According to the instructions you construct a new rectangle with width 2 feet shorter than y and length 3 feet longer than x. Thus the new rectangle is y - 2 feet by x + 3 feet. You are also told that one of these dimensions is 6/5 times the other. But 6/5 > 1 and x + 3 > y - 2 and hence it must be that

(x + 3) = 6/5 (y - 2).

The area of the new rectangle is (x + 3)(y - 2) square feet which we are told is 250 square feet larger than the original rectangle. Thus

(x + 3)(y - 2) - xy = 250

Solve these two equations for x and y.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.