Question

In the given $∆ABC$ the length of side $AB$ and $AC$ is same$\left(i.eb=c\right)$ and $60°<A<90°$

• A. $b<a<b\sqrt{3}$
• B. $c<a<c\sqrt{2}$
• C. $b<a<2b$
• D. $\frac{c}{3}<a<3c$

Answer 1

The correct option is B

$c<a<c\sqrt{2}$

Explanation for correct answer:

The correct option is Option $\left(B\right)$ $c<a<\sqrt{2}c$:

When $\angle A=60°$ and $b=c$, then $∆ABC$ is equilateral.

$\Rightarrow a=b=c$

When $A=90°,$then $∆ABC$ is an isosceles right angled triangle and

$\Rightarrow a=\sqrt{2}b$or $a=\sqrt{2}c$

$\therefore 60°<A<90°$

$\Rightarrow c<a<\sqrt{2}c$

Therefore, option $\left(B\right)$ is correct answer.