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ACT
ACT Math Section

Pathway Width Calculation in Rectangular Field

Hard Preparing For Higher Math Number And Quantity

A farmer has a rectangular field that measures 120 meters by 80 meters. He wants to create a pathway that is uniform in width around the outside of the field to increase its total area. If the total area of the field including the pathway needs to be 12,000 square meters, what should be the width of the pathway?

Let the width of the pathway be represented as $$x$$. The area of the field is originally $$120 imes 80$$, so the area after adding the pathway will be $$A = (120 + 2x)(80 + 2x)$$.

Your task is to determine the value of $$x$$ such that the total area equals 12,000 square meters.

Hint

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