Triangle sides in fractional ratio — find the smallest side from perimeter: The sides of a triangle are in the ratio 1/3 : 1/4 : 1/5 and its perimeter is 94 cm. Find the length of the smallest side.

Introduction / Context:Ratios can be fractional; you can scale them by a common factor to obtain actual sides. The perimeter ties down the scale.

Given Data / Assumptions:Side ratios: 1/3 : 1/4 : 1/5; Perimeter = 94 cm.

Concept / Approach:Let the sides be k/3, k/4, k/5. Then sum = k*(1/3 + 1/4 + 1/5) = k*(47/60). Set this equal to 94 to solve k, then select the smallest side.

Step-by-Step Solution:k*(47/60) = 94 ⇒ k = 94*60/47 = 120Sides: 120/3 = 40, 120/4 = 30, 120/5 = 24Smallest side = 24 cm

Verification / Alternative check:Sum 40 + 30 + 24 = 94 ✓ and the ratio reduces back to 1/3 : 1/4 : 1/5 when scaled by 120.

Why Other Options Are Wrong:They do not match the computed side lengths from the ratio and perimeter.

Common Pitfalls:Inverting the fractional ratios or using 1:3:4:5 erroneously.

Final Answer:24 cm