Question

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?

$100$

$200$

$300$

$400$

$500$

Solution:

The current length of the fence is $2(50 + 10) = 2 \cdot 60 = 120$ feet. If all the sides become the same, then each side length is $120 \div 4 = 30$ feet. As such, the area of the square is then $30^2 = 900$ square feet. Note that the original area of the garden is $50 \cdot 10 = 500$ square feet.

Therefore, the difference is $900 - 500 = 400$ square feet.

Thus, D is the correct answer.

1999 AMC 8 Problem 5

Solution:

Problem 5 in Other Years