Math CentralQuandaries & Queries


Question from Becky, a student:

A rectangle has an area of 48 square inches and perimeter of 32 inches. Find the dimensions of the rectangle.

Hi Becky,

You are asked for the dimensions of the rectangle which means the length and the width so I would start by saying

Let the length of the rectangle be $L$ inches and the width $W$ inches.

The area of a rectangle is the length times the width so using $L$ and $W$ what you know is

\[L \times W = 48 \mbox{ square inches.}\]

Using $L$ and $W$ write an equation for the perimeter of the rectangle. Solve this equation for $L$ in terms of $W,$ substitute into the first equation and solve the resulting equation for $W.$

Write back if you need more assistance,

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