Question

Two square sheets of cardboard used for making book covers differ in area by 81 square inches. An edge of the large square is 3 inches greater than an edge of the smaller square. Find the length of an edge of the smaller square.

Answer 1

Let x be the smaller sheet.
Smaller sheet = x
Larger sheet = x + 3

Area of the smaller sheet = x²
Area of the larger sheet = (x + 3)²

The difference is 81 in²
(x + 3)² - x² = 81
x² + 6x + 9 - x² = 81
6x + 9 = 81
6x = 72
x = 12 inches

Answer: The edge of the smaller square is 12 inches.