Question

The sides of a triangle are in the ratio $$\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$$ and its perimeter is $$91 \text{ cm}$$. Find the lengths of the sides of the triangle.

Answer 1

Simplify the given ratio $$\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$$ by multiplying each term by the L.C.M. of 2, 3 and 4, which is 12:

$$\left(\frac{1}{2} \times 12\right) : \left(\frac{1}{3} \times 12\right) : \left(\frac{1}{4} \times 12\right) = 6 : 4 : 3$$ 

Let the sides be $$6x$$, $$4x$$ and $$3x$$. 

Perimeter = $$6x + 4x + 3x = 13x = 91\text{ cm}$$.

$$x = \frac{91}{13} = 7$$ 

Lengths of the sides:

First side = $$6 \times 7 = 42\text{ cm}$$

Second side = $$4 \times 7 = 28\text{ cm}$$

Third side = $$3 \times 7 = 21\text{ cm}$$

Therefore, the sides of the triangle are $$42\text{ cm}$$, $$28\text{ cm}$$ and $$21\text{ cm}$$.