Question

Mark (✓) against the correct answer in each of the following:
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) 30 cm²
(b) 45 cm²
(c) 60 cm²
(d) 78 cm²
Figure

Answer 1

(c) 60 cm<sup>2

$$\begin{gathered} \mathrm{Area}\mathrm{of}\text{an}\mathrm{isosceles}\mathrm{triangle}=\frac{1}{4}b\sqrt{4a^2-b^2} \\ \text{H}\mathrm{ere},a=\mathrm{equal}\mathrm{sides}\mathrm{and}b=\mathrm{third}\mathrm{side} \\ \mathrm{Here},a=13\mathrm{cm}\mathrm{and}b=24\mathrm{cm} \\ \mathrm{Therefore},\text{a}\mathrm{rea}=\frac{1}{4}\times 24\times \sqrt{4\times {13}^2-{12}^2} \\ =6\times \sqrt{4\times {13}^2-{24}^2} \\ =6\times \sqrt{4\times 169-576} \\ =6\times \sqrt{676-576} \\ =6\times \sqrt{100} \\ =6\times 10 \\ =60{\mathrm{cm}}^2 \end{gathered}$$</sup>