Question

For an isosceles triangle having base = 12 cm and each of the equal sides equal to 10 cm, the height is
(a) 12 cm
(b) 16 cm
(c) 6 cm
(d) 8 cm

Answer 1

(d) 8 cm
$$\begin{gathered} \mathrm{Height}\mathrm{of}\mathrm{isosceles}\mathrm{triangle}=\frac{1}{2}\sqrt{4a^2-b^2} \\ =\frac{1}{2}\sqrt{4{\left(10\right)}^2-{12}^2}\left(a=10\mathrm{cm}\mathrm{and}b=12\mathrm{cm}\right) \\ =\frac{1}{2}\times \sqrt{400-144} \\ =\frac{1}{2}\times \sqrt{256} \\ =\frac{1}{2}\times 16 \\ =8\mathrm{cm} \end{gathered}$$