Question

The base of an isosceles triangle is $\frac{4}{3}cm$. The perimeter of the triangle is $4\frac{2}{15}cm$. What is the length of either of the remaining equal sides?
[3 marks]

Answer 1

Let the length of equal sides of an isosceles triangle be $xcm$.
We know,
The perimeter of a triangle = Sum of all its three sides
[1 mark]
$\Rightarrow 4\frac{2}{15}=\frac{4}{3}+x+x$
$\Rightarrow \frac{62}{15}=\frac{4}{3}+2x$
[1 mark]
$\Rightarrow \frac{62}{15}-\frac{4}{3}=\frac{4}{3}-\frac{4}{3}+2x$
[Subtracting $\frac{4}{3}$ from both the sides]
$\Rightarrow \frac{62-20}{15}=2x$
$\Rightarrow \frac{42}{15}=2x$
$\Rightarrow \frac{42}{15\times 2}=\frac{2x}{2}$ [Dividing both sides by $2$]
$\Rightarrow \frac{7}{5}=x$
$\Rightarrow x=1\frac{2}{5}cm$
Hence, each equal side of an isosceles triangle is $1\frac{2}{5}cm.$
[1 mark]