Question

Perimeter of an isosceles triangle is $40cm$. The base is two third of the sum of sides. Find the length of each side.

Answer 1

In an isoceles triangle, two sides are equal.
Let, the length of equal sides be $x$.
Length of base =$\left(\frac{2}{3}\right)$ of sum of sides$(x+x)$ $=\left(\frac{2}{3}\right)$ of $\left(2x\right)=\frac{4x}{3}$
( Since the question is not clear, whether it is $\frac{2}{3}$ of sum of two equal sides or all sides, I will assume that it is $\frac{2}{3}$ of sum of two equal sides)
So, $x+x+\frac{4x}{3}=40$
$\frac{3x+3x+4x}{3}=40$
$\Rightarrow \frac{10x}{3}=40$
$\Rightarrow x=40\times \frac{3}{10}$
$\Rightarrow x=12$
Therefore, sides are $12,12$ and $\frac{4x}{3}=\frac{4\times 12}{3}=16$.