In ∆ABC, D and E are the points on sides AB and AC…

In ∆ABC, D and E are the points on sides AB and AC, respectively and DE||BC. BC = 8cm and DE = 5cm. If the area of ∆ ADE = 45 cm², then what is the area (in cm²) of ∆ABC?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e 115.2.

Here DE is parallel to BC so one can say that $\triangle$ ADE and $\triangle$ ABC are similar.

$\frac{Area \ of \ \triangle ADE}{Area \ of \ \triangle ABC}= (\frac{5}{8})^2$

$\frac{45}{\triangle ABC} = \frac{25}{64}$

Area of $\triangle$ ABC = 115.2 cm².

SSC CGL 2021 PYQ — Question 75