Question

∆ABC is an isosceles triangle with AB = AC = 13 cm and the length of altitude from A on BC is 5 cm. Then, BC = ?
(a) 12 cm
(b) 16 cm
(c) 18 cm
(d) 24 cm

Answer 1

(d) 24 cm

In triangle ABC, let the altitude from A on BC meets BC at D.
We have:
AD = 5 cm, AB = 13 cm and D is the midpoint of BC.
Applying Pythagoras theorem in right-angled triangle ABD, we get:
$$\begin{gathered} A{B}^2=A{D}^2+B{D}^2 \\ \Rightarrow B{D}^2=A{B}^2-A{D}^2 \\ \Rightarrow B{D}^2={13}^2-5^2 \\ \Rightarrow B{D}^2=169-25 \\ \Rightarrow B{D}^2=144 \\ \Rightarrow BD\hspace{0.17em}=\sqrt{144}=12\mathrm{cm} \end{gathered}$$

Therefore, BC = 2BD = 24 cm