Question

Parth went to Coorg on a holiday. He wanted to make a tent using a canvas cloth and a few bamboo sticks as support. Initially, he made a sketch of the tent as shown in the figure. He wanted to make the tent as an exact replica of the sketch. So, he placed the bamboo stick DE parallel to the ground BC and AG perpendicular to the ground. Let’s analyse his sketch.


If Parth considers AE = 2 ft, then the length of the stick DE that he needs to use is ___ ft.

[1 mark]

• A. 3
• B. 4
• C. $\frac{12}{5}$
• D. $\frac{16}{5}$

Answer 1

The correct option is C $\frac{12}{5}$

Since DE is parallel to BC,

$\frac{AE}{EC}=\frac{AD}{DB}=\frac{2}{3}$

$\Rightarrow \frac{AE}{EC}=\frac{2}{3}$

We have AE = 2

$\Rightarrow \frac{2}{EC}=\frac{2}{3}$

$\Rightarrow EC=3$

$AC=AE+EC=2+3=5$

Comparing $\Delta ABGand\Delta AGC$,

Since AB = AC = 5, $\angle ABC=\angle ACB$ (Opposite angles of equal angles are equal.)
$\angle AGC=\angle AGC={90}^{\circ }$
$\therefore \Delta AGB\sim \Delta AGC$ (AA similarity)

Ratio of corresponding sides $=\frac{AB}{AC}=\frac{BG}{GC}=\frac{AG}{AG}=1$

$\frac{BG}{GC}=1\Rightarrow GC=BG=3$

BC = BG + GB = 3 + 3 = 6

Since $\Delta ADE\sim \Delta ABC,$
$\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}$
$\frac{DE}{BC}=\frac{AD}{AB}=\frac{2}{5}$

$\Rightarrow \frac{DE}{BC}=\frac{2}{5}$

$\Rightarrow \frac{DE}{6}=\frac{2}{5}$

$\therefore DE=\frac{12}{5}$