Question

In $∆\mathrm{ABC}$, if $\angle B=\angle C=45°$, which of the following is the longest side?

• A. $AB$
• B. $AC$
• C. $BC$
• D. None of these

Answer 1

The correct option is C

$BC$

Explanation for the correct option:

Find the longest side

By the angle sum property of triangles,
$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°$

By substituting known values,
$\angle \mathrm{A}+45°+45°=180°$
$\Rightarrow \angle \mathrm{A}=180°-90°$
$\Rightarrow \angle \mathrm{A}=90°$

Hence, $∆\mathrm{ABC}$ is right angled at $\mathrm{A}$.

We know that the side opposite to the greater angle is greater.

Also, hypotenuse is the largest side in a right $\Delta$.
Thus, $\mathrm{BC}$ is the longest side.

Therefore, option (C) is correct answer