# The base of an isosceles triangle is 16 cm and its area is 48 cm2.

Question:

The base of an isosceles triangle is 16 cm and its area is 48 cm2. The perimeter of the triangle is
(a) 41 cm
(b) 36 cm
(c) 48 cm
(d)
324 cm

Solution:

(b) 36 cm

Let $\triangle P Q R$ be an isosceles triangle and $P X \perp Q R$.

Now,

Area of triangle $=48 \mathrm{~cm}^{2}$

$\Rightarrow \frac{1}{2} \times Q R \times P X=48$

$\Rightarrow h=\frac{96}{16}=6 \mathrm{~cm}$

Also,

$Q X=\frac{1}{2} \times 24=12 \mathrm{~cm}$ and $P X=12 \mathrm{~cm}$

$P Q=\sqrt{Q X^{2}+P X^{2}}$

$a=\sqrt{8^{2}+6^{2}}=\sqrt{64+36}=\sqrt{100}=10 \mathrm{~cm}$

$\therefore$ Perimeter $=(10+10+16) \mathrm{cm}=36 \mathrm{~cm}$