Question

In the figure, given alongside, $\angle APQ=\angle C$. Hence, If AQ = 9 cm, BP = 3 cm and AP = 15 cm; find AC in cm

Answer 1

Given: $\angle APQ=\angle C$

In $△APQ$ and $△ABC$

$\angle PAQ=\angle BAC$ (Common angle)

$\angle APQ=\angle C$ (Given)

$\angle AQP=\angle B$ (third angle)

Thus, $△APQ\sim △ACB$ (AAA rule)

Hence, $\frac{AP}{AC}=\frac{AQ}{AB}$

$\frac{15}{AC}=\frac{9}{15+3}$

$AC=\frac{15\times 18}{9}$

$AC=30$ cm