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 :
$\frac{24}{4} \times \sqrt{4(13)^{2}-24^{2}}$
$=6 \times \sqrt{676-576}$
$=6 \times \sqrt{100}$
$=6 \times 10$
$=60 \mathrm{~cm}^{2}$
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