Math CentralQuandaries & Queries


Question from Becca, a student:

A rectangle is 8 feet long and 6 feet wide. If each dimension is increased by the same number of feet, the area off the new rectangle formed is 32 square feet more than the area of the original rectangle. By how many feet was each dimension increased? I need a diagram and 5 or more sentences for an explanation. Thanks!

Hi Becca.

Try this with algebra: Let x be the number of feet each dimension was increased by. Then the problem is to find x.

The area of a rectangle is the length times width. The initial rectangle is 8 x 6 = 48 square feet. The new rectangle is 32 square feet more. That's 48 + 32 = 80 square feet.

So the new rectangle's width is the initial width (6 ft) plus the increase (x). That's 6+x. The length is 8+x. That means (6+x)(8+x) is the new area, which we said is 80 square feet.

So (6+x)(8+x) = 80.

Solve for x. I'll leave you to draw the diagram.

Stephen La Rocque.>

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