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? (A) 100 (B) 200 (C) 300 (D) 400 (E) 500

solution

(D) 400 square feet: The area of the garden was 500 square feet(50£10) and its perimeter was 120 feet, 2 £ (50 + 10). The square garden is also enclosed by 120 feet of fence so its sides are each 30 feet long. The square garden's area is 900 square feet (30 £ 30). and this has increased the garden area by 400 square feet.