Math CentralQuandaries & Queries


Question from Sugavanas, a student:

If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is 4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle.

Hi Sugavanas,

The key to these word problems is to read them carefully and decide which quantities to express as variables. You are to find the dimensions (length and width) of the rectangle so

let $L$ be the width of the rectangle and let $W$ be its width.

Read the first sentence carefully. It says the length exceeds the width ny 5 m, or in terms of the variables $L$ is 5 m more than $W.$ As an equation that's

\[L = W + 5\]

In the second sentence you are told to increase the width $W$ by 1 m and decrease the length $W + 5$ by 2 m. What are the new dimensions?

The area of a rectangle is the length times the width so the area of the original rectangle is $(W + 5) \times W$ square meters. What is the area of the modified rectangle? This is 4 sq m less than $(W + 5) \times W.$ Solve for $W.$

Write back if you need more assistance,


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