Question

If AC = 13.5 cm and CD = 4.5 cm ; calculate the length of BC.

Answer 1

In $△ADC$ and $△ABC$,
$\angle ADC=\angle BAC$ (Each ${90}^{\circ }$)
$\angle ACD=\angle ACB$ (Common angle)
$\angle DAC=\angle ABC$ (Third angle)
Thus, $△ADC\sim △BAC$ (AAA postulate)
Thus, $\frac{AC}{BC}=\frac{CD}{AC}$ (Corresponding sides)
$\frac{13.5}{BC}=\frac{4.5}{13.5}$
$BC=\frac{13.5\times 13.5}{4.5}$
$BC=40.5$ cm