AMC 12 Mock Exam 2 Problem 1

Problem 1 of 25

A rectangular garden is $5$ meters longer than it is wide. A gravel path $1$ meter wide is built around the outside of the garden, so that the garden and the path together form a larger rectangle. The path alone covers $62$ square meters. What is the area of the garden, in square meters?

Show solution

Solution

Let the garden be $w$ by $w+5$ . With the path, the outer rectangle is $(w+2)$ by $(w+7)$ , so the path's area is $(w+2)(w+7)-w(w+5)=4w+14=62,$ giving $w=12$ . The garden is $12$ by $17$ , with area $\boxed{204}$ .

Tagged: area word problem leading to a linear equation

Answer choices

Solution