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Problem 555

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

3. The area of a rectangle is $2255 \mathrm{~cm}^{2}$ . If one side of the rectangle is reduced by $6 \mathrm{~cm}$ , the area of the rectangle will be $2009 \mathrm{~cm}^{2}$ . What is the perimeter of the original rectangle?

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

3. Let $a$ and $b$ be the lengths of the sides of a rectangle. If side $b$ is reduced by $6 \mathrm{~cm}$ , the area of the new rectangle is $a \cdot (b-6) = a \cdot b - 6 \cdot a$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.