# 2015 AMC 10A Problems/Problem 20

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## Problem

A rectangle has area and perimeter , where and are positive integers. Which of the following numbers cannot equal ?

## Solution

Let the rectangle's length and width be and . Its area is and the perimeter is .

Then . Factoring, this is .

Looking at the answer choices, only cannot be written this way, because then either or would be .

So the answer is .