# Each of the equal sides of an isosceles triangle is 13 cm and its base is 24 cm. The area of the triangle is

Question:

Each of the equal sides of an isosceles triangle is 13 cm and its base is 24 cm. The area of the triangle is
(a) 156 cm2
(b) 78 cm2
(c) 60 cm2
(d) 120
cm2

Solution:

(c) $60 \mathrm{~cm}^{2}$

Area of isosceles triangle $=\frac{b}{4} \sqrt{4 a^{2}-b^{2}}$

Here,

$a=13 \mathrm{~cm}$ and $b=24 \mathrm{~cm}$

Thus, we have :

$\frac{24}{4} \times \sqrt{4(13)^{2}-24^{2}}$

$=6 \times \sqrt{676-576}$

$=6 \times \sqrt{100}$

$=6 \times 10$

$=60 \mathrm{~cm}^{2}$