Question

The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 104 cm. the length of the longest side (in cm) is

Answer 1

let x be a constant, then,
first side =
$\frac{x}{2}$
second side =
$\frac{x}{3}$
third side =
$\frac{x}{4}$
then, A T Q. --
$\frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 104$
$x( \frac{6 + 4 + 3}{12}) = 104$
$x( \frac{13}{12} ) = 104$
$x = 104 \times \frac{12}{13}$
$x = 8 \times 12$
$x = 96$

Now longest side is
$\frac{x}{2}$
so, longest side is
$\frac{96}{2} = 48 \: \: \: cm$