Question

An isosceles triangle have unequal side to be $16$ cm and the altitude drawn to this side has the length as $6$ cm then what is the perimeter of the given triangle?

• A. $20$ cm
• B. $36$ cm
• C. $26$ cm
• D. $30$ cm

Answer 1

The correct option is B $36$ cm

We know that in an isosceles triangle, a perpendicular, drawn from the apex vertex, bisects the base.
So,
$BD=8$ cm
Now, applying pythagorasd theorem, we get
$A{B}^2=B{D}^2+A{D}^2$
$A{B}^2=8^2+6^2$
$AB=\sqrt{64+36}$
$AB=\sqrt{100}$
$AB=10$ cm
As, $△ABC$ is Isosceles triangle so,
$AB=AC$
$AC=10$ cm
So, $\text{(perimeter of the triangle})=10+10+16$
$\text{perimeter of triangle}=36$ cm
Hence, option $\left(b\right)$ correct.