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.


Now that he calculated the length of the stick DE, he needs to fix it at the correct position. So, the distance of DE from the apex of the tent, A, i.e., AF = __ ft

[1 mark]

• A. 2
• B. 3
• C. $\frac{6}{5}$
• D. $\frac{8}{5}$

Answer 1

The correct option is D $\frac{8}{5}$

In order to find AF, we need to find AG first.

By applying the Pythagoras theorem in $\Delta ABG,$

$A{G}^2+B{G}^2=A{B}^2$
$\Rightarrow A{G}^2+3^2=5^2$
$\Rightarrow AG=4$

Since DF is parallel to BG in the $\Delta ABG,$ we can write:
$\frac{AD}{DB}=\frac{AF}{FG}$ (DF divides AG and AB in the same ratio.)

$\Rightarrow \frac{DB}{AD}=\frac{FG}{AF}$

Adding 1 on both sides of the equation,

$\Rightarrow \frac{DB}{AD}+1=\frac{FG}{AF}+1$

$\Rightarrow \frac{DB+AD}{AD}=\frac{FG+AF}{AF}$

$\Rightarrow \frac{AB}{AD}=\frac{AG}{AF}$

$\Rightarrow \frac{5}{2}=\frac{4}{AF}$

$\therefore AF=\frac{8}{5}units$