The sides of a triangle are proportional to 1/2, 1/3, and 1/4. If the triangle's perimeter measures 52 cm, what is the length of its shortest side?

Explanation

First, express the side ratios with a common denominator: 1/2 = 6/12, 1/3 = 4/12, and 1/4 = 3/12, so the ratio simplifies to 6:4:3. The sum of the ratio parts is 6 + 4 + 3 = 13. Each part equals 52 ÷ 13 = 4 cm. Therefore, the sides measure 6 × 4 = 24 cm, 4 × 4 = 16 cm, and 3 × 4 = 12 cm. The shortest side is 12 cm.