Question

The base of an isosceles triangle is 6 cm and each of its equal sides is 5 cm. The height of the triangle is
(a) 8 cm
(b) $\sqrt{30}\mathrm{cm}$
(c) 4 cm
(d) $\sqrt{11}\mathrm{cm}$

Answer 1

(c) 4 cm
$$\begin{gathered} \mathrm{Height}\mathrm{of}\mathrm{isosceles}\mathrm{triangle}=\frac{1}{2}\sqrt{4a^2-b^2} \\ =\frac{1}{2}\sqrt{4{\left(5\right)}^2-6^2}\left(a=5\mathrm{cm}\mathrm{and}b=6\mathrm{cm}\right) \\ =\frac{1}{2}\times \sqrt{100-36} \\ =\frac{1}{2}\times \sqrt{64} \\ =\frac{1}{2}\times 8 \\ =4\mathrm{cm} \end{gathered}$$