Question

In the given figure, AB and DE are perpendicular to BC. [3 MARKS]

i) Prove that $\Delta ABC\sim \Delta DEC$
ii) If AB = 6 cm, DE = 4 cm and AC = 15 cm, calculate CD.
iii) Find the ratio of the area of $\Delta ABC$ : area of $\Delta DEC$

Answer 1

Each Part: 1 Mark

i)

In $\Delta ABC$ and $\Delta DEC$,
$\angle ABC=\angle DEC$ $[\because AB\perp BCandDE\perp BC]$
$\angle BCA=\angle DCE$ [Common]
$\therefore \Delta ABC\sim \angle DEC$ [By AA similarity axiom]

ii) $\frac{AB}{DE}=\frac{AC}{CD}\Rightarrow \frac{6}{4}=\frac{15}{CD}$
$\Rightarrow CD=10cm$

iii) $\frac{Areaof\Delta ABC}{Areaof\Delta DEC}=\frac{A{B}^2}{D{E}^2}$
$=\frac{6^2}{4^2}=\frac{36}{16}=\frac{9}{4}$