Question

The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4. If its perimeter is 52 cm, the length of the smallest side is _____ .

• A. 9 cm
• B. 10 cm
• C. 11 cm
• D. 12 cm

Hint:

When solving ratio problems, find the common multiple to simplify the ratio and use the given total (like the perimeter) to solve for the unknowns.

Answer 1

The Correct Option is D

Let the sides of the triangle be \( x, y, z \), where their ratio is given as \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \). The least common multiple of 2, 3, and 4 is 12. Thus, the sides are \( 6k, 4k, 3k \), where \( k \) is the common multiplier. The perimeter is 52 cm, so: \[ 6k + 4k + 3k = 52 \] \[ 13k = 52 \] \[ k = 4 \] The smallest side is \( 3k = 3 \times 4 = 12 \, \text{cm} \).