Question

In an isosceles triangle ABC, if AB = AC = 25 cm and BC = 14 cm, the measure of altitude from A on BC is

(a) 20 cm
(b) 22 cm
(c) 18 cm
(d) 24 cm

Answer 1

Given: In an isosceles triangle ABC, AB = AC = 25 cm and BC = 14cm.

To find: Measure of altitude from A on BC

Since AD ⊥ BC, so BD = CD = $\frac{\mathrm{BC}}{2}=\frac{14\mathrm{cm}}{2}=7\mathrm{cm}$

In right ∆ABD,

$$\begin{gathered} {\mathrm{AB}}^2={\mathrm{AD}}^2+{\mathrm{BD}}^2 \\ \Rightarrow {\mathrm{AD}}^2={\mathrm{AB}}^2-{\mathrm{BD}}^2 \\ \Rightarrow {\mathrm{AD}}^2={25}^2-7^2=625-49=576 \\ \Rightarrow \mathrm{AD}=24\mathrm{cm} \end{gathered}$$

We got the result as .