Question

The perimeter of an isosceles triangle is 42 cm and its base 1$\frac{1}{2}$ times its congruent sides. Find
(i) the length of congruent sides of a triangle

Answer 1

(i) Let the length of the congruent sides be x cm.
Then length of the base = $1\frac{1}{2}x=\frac{3}{2}x$ cm
Perimeter of the isosceles triangle = sum of all sides
$\Rightarrow$ 42 = x + x + $\frac{3}{2}x$
$$\begin{gathered} \Rightarrow 42=2x+\frac{3}{2}x \\ \Rightarrow 42=\frac{7x}{2} \\ \Rightarrow x=12\mathrm{cm} \end{gathered}$$

∴ Length of the congruent sides = 12 cm