   SEARCH HOME Math Central Quandaries & Queries  Question from Nawal, a student: A rectangle is twice as long as it is wide. If both its dimensions are increased by 4 m, its area is increased by 88 m ^ 2. Find the dimensions of the original rectangle. Nawal,

You need to read the question carefully, convert the English sentences into mathematical expressions and then put the expressions together to answer the question. The question asks for the dimensions of the rectangle so I am going to give the dimensions names. Let L be the length of the rectangle and W be its width. Since the units mentioned are metres and square metres I am going to let L and W be measured in metres.

A rectangle is twice as long as it is wide.

This converts to L = 2 W

The sentence "If both its dimensions are increased by 4 m, its area is increased by 88 m2." compares the area of the original rectangle to the area of a larger rectangle. The area of the original rectangle is L × W m2. The larger rectangle has both dimensions increased by 4 metres so it is L + 4 metres by W + 4 metres and thus its area is (L + 4) × (W + 4) square metres. Thus the sentence "If both its dimensions are increased by 4 m, its area is increased by 88 m2." says

(L + 4) × (W + 4) is 88 m2 more than L × W

that is

(L + 4) × (W + 4) = L × W + 88

From the first sentence you can substitute L = 2 W and then solve for W.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.