Question

In the given figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm, AD = 4 cm, find CD.

Answer 1

It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse.

$$\begin{gathered} \mathrm{In}△DBA\mathrm{and}△DCB,\mathrm{we}\mathrm{have}: \\ \angle BDA=\angle CDB \\ \angle DBA\hspace{0.17em}=\angle DCB=90° \\ \mathrm{Therefore},\mathrm{by}\mathrm{AA}\mathrm{similarity}\mathrm{theorem},\mathrm{we}\mathrm{get}: \\ △DBA~△DCB \\ \Rightarrow \frac{BD}{CD}=\frac{AD}{BD} \\ \Rightarrow CD=\frac{B{D}^2}{AD} \end{gathered}$$

CD = $\frac{8\times 8}{4}=16$ cm