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.

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.