Question

In the given figure, AB and DE are perpendicular to BC. If AB = 9 cm, DE = 3 cm and AC = 24 cm, calculate AD. [4 MARKS]

Answer 1

Applying theorems: 2 Marks
Calculation: 2 Marks

Given: $AB\perp BC,DE\perp BC,AB=9cm,DE=3cm$ and $AC=24cm$
In $\Delta ABC$ and $\Delta DEC$,
$\angle ABC=\angle DEC$ [Each of ${90}^{\circ }$]
$\angle ACB=\angle DCE$ [Common]
$\therefore \Delta ABC\sim \Delta DEC$ [By AA similarity]
Now $\frac{AB}{DE}=\frac{AC}{DC}$
$\Rightarrow \frac{9}{3}=\frac{24}{DC}$
$\Rightarrow DC=\frac{24\times 3}{9}cm$
$=8cm$
Hence, AD = (24-8)cm = 16 cm