The sides of a triangle are in the ratio 1/3 : 1/4 : 1/5 and its perimeter is 94 cm. What is the length of the smallest side?

Introduction / Context:
Ratios with fractional terms can be cleared by multiplying all terms by the least common multiple (LCM) of the denominators. This produces integer parts that sum to a total number of parts matching the perimeter scale.

Given Data / Assumptions:

• Sides ∝ 1/3 : 1/4 : 1/5
• Perimeter = 94 cm

Concept / Approach:
Multiply each term by LCM(3,4,5) = 60 to obtain equivalent integer parts: 20 : 15 : 12. Sum these parts; each side is then proportional to its part times a common multiplier derived from the perimeter.

Step-by-Step Solution:
Convert ratio: (1/3 : 1/4 : 1/5) × 60 = 20 : 15 : 12Total parts = 20 + 15 + 12 = 47Common multiplier = perimeter / total parts = 94 / 47 = 2Smallest side corresponds to part 12 ⇒ 12 * 2 = 24 cm

Verification / Alternative check:
Other sides: 20*2 = 40 cm, 15*2 = 30 cm; sum 40 + 30 + 24 = 94 cm, confirming correctness.

Why Other Options Are Wrong:
They do not match the required scaling once the fractional ratio is converted to integers and matched to the perimeter.

Common Pitfalls:
Adding fractions directly or confusing which side is “smallest” after clearing denominators; the smallest is the 1/5 term (becoming 12 parts).

Final Answer:
24 cm