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

Answer 1

(c) 60 cm²
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{isosceles}\mathrm{triangle}=\frac{b}{4}\sqrt{4a^2-b^2} \\ \mathrm{Here}, \\ a=13\mathrm{cm}\mathrm{and}b=24\mathrm{cm} \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \frac{24}{4}\times \sqrt{4(13{)}^2-{24}^2} \\ =6\times \sqrt{676-576} \\ =6\times \sqrt{100} \\ =6\times 10 \\ =60{\mathrm{cm}}^2 \end{gathered}$$