The sides of a triangle are in the ratio \(\displaystyle\frac{1}{3}:\frac{1}{4}:\frac{1}{5}\). If the semi-perimeter of the triangle is 47 cm, then what is the length of the longest side?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 40 cm
A ratio of fractions is turned into whole numbers by multiplying every term by the LCM of the denominators; the perimeter is twice the semi-perimeter.
LCM of 3, 4 and 5 is 60: \(\displaystyle \frac{1}{3}:\frac{1}{4}:\frac{1}{5}=20:15:12\)
Perimeter \(=2\times47=94\) cm
Sides \(20k\), \(15k\), \(12k\): \(47k=94\), so \(k=2\)
Longest side \(=20\times2=40\) cm