Question

In $△ABC$, $\angle B=\angle C$ and $AB=1.5\left(BC\right)$. If perimeter of the triangle is 8 cm, then AC is equal to ______cm.

Answer 1

Given, in $△ABC$, $\angle B=\angle C$.
$\Rightarrow AB=AC$ (sides opposite to equal angles are equal)
Let BC be x.
Given, $AB=1.5\left(BC\right)$
$\Rightarrow 1.5\left(BC\right)=AC$
$\Rightarrow 1.5x=AC$
Total perimeter of the triangle = 8 cm.
$\Rightarrow AB+AC+BC=8\text{cm}$
$\Rightarrow 1.5x+1.5x+x=8\text{cm}$
$\Rightarrow 4x=8\text{cm}$
$\Rightarrow x=2\text{cm}$
$\therefore AC=1.5x=1.5\times 2=3\text{cm}$