In the given figure, AP is equal to

Question

$\begin{array}{1 1} 7\;cm \\ 6\;cm \\ 5.5 \;cm \\ 5\;cm \end{array} $

Answer 1

Solution :

In triangles APB and CPD,

$\angle APB = \angle CPD$ [Vertically opposite angles]

$\angle BAP = \angle ACD $ [Alternate angles as $AB \parallel CD$

$\Delta APB \approx \Delta CPD$ [AA similarity]

$\large\frac{AB}{CD} =\frac{CP}{AP}$

$\large\frac{4}{6} =\frac{AP}{7.5}$

$AP= \large\frac{7.5 \times 4 }{6}$$ = 5 \;cm$