Question

Consider isosceles triangle $ABC$, in which $\angle ABC=\angle ACB$ , $AB=2BC$ and $AB=8cm$ . What is the perimeter of the $△ABC$?

• A. $24cm$
• B. $32cm$
• C. $20cm$
• D. $18cm$

Answer 1

Answer: (C)

$20cm$

$△ABC$ is an isosceles triangle.

Gi en that $\angle ABC=\angle ACB$, $AB=2BC$ and $AB=8$ cm$

So, $AB=AC=8$ cm

$\Rightarrow BC=\frac{AB}{2}=4$ cm

Perimeter of $△ABC=8+8+4=20$ cm.

Here, $△ABC$ is an isosceles triangle.

Given, $\angle ABC=\angle ACB$, $AB=2BC$ and $AB=8cm$.

We know, by isosceles triangle property, angles opposite to equal sides are equal.

Then, So, $AB=AC=8cm$.

Since $AB=2BC$,

$\Rightarrow BC=\frac{AB}{2}=4cm$.

Thus, perimeter of $△ABC=8+8+4=20cm$.

Hence, option $C$ is correct.