1999 AMC 8 Problems/Problem 5

Problem

A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?

$\text{(A)}\ 100 \qquad \text{(B)}\ 200 \qquad \text{(C)}\ 300 \qquad \text{(D)}\ 400 \qquad \text{(E)}\ 500$

Solution

The perimeter of the rectangular garden is $2(50+10)=120$ feet. A square with this perimeter has sidelength $120/4=30$ feet. The area of the rectangular garden is $(50)(10=500$ and the area of the square garden is $(30)(30)=900$ , so the area increases by $900-500=\boxed{\text{(D)}\ 400}$ .

1999 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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1999 AMC 8 Problems/Problem 5

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