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Problem

A rectangular garden 60 feet long and 20 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 $(60)(10)=600$ and the area of the square garden is $(30)(30)=900$, so the area increases by $900-600=\boxed{\text{(C)}\ 300}$.

See Also

1999 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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