The length of a rectangle is 10 inches greater than the width. The area of the rectangle is 75 square inches. Find the dimensions.

Question

The length of a rectangle is 10 inches greater than the width. The area of the rectangle is 75 square inches. Find the dimensions.

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Answer 1

Hi Blanca,

The answer is 5" X 15"

The rectangle has (width = x) and (length = x + 10). It also says that the area of the rectangle is 75 in². Remember that (Area = width x length), so you can set up the equation as:

75 = x (x+10)

This can be simplified further:

75 = x² + 10x

0 = x² + 10x - 75

0 = (x+15)(x-5)

From here, you find that x = -15 and +5. Since a rectangle cannot have a negative width or length, the only answer that makes sense is 5 inches. Plug 5 in for x in the original dimensions of the rectangle (Width = x ; Length = x + 10) and you'll find that the dimensions are 5 inches X 15 inches

Hope this helps!