jmc

Question

A 40-foot by 10-foot rectangular garden is enclosed by a fence. To make the garden larger, while using the same amount of fencing, its shape is changed to a square. How many square feet larger than the old garden is the new garden?

Accepted Answer

The original garden has an area of 40 10=400 ft^2. Its perimeter is 40+10+40+10=100 ft, so a square fence using the same amount of fencing has sides of length 25 ft and an area of 25 25 = 625 ft^2. The increase in area is thus 625 - 400 = 225 square feet.