Question

In ΔABC, D and E are the points on sides AB and AC, respectively and DE ∥ BC. BC = 8 cm and DE = 5 cm. If the area of ΔADE = 45 cm², then what is the area (in cm²) of ΔABC ?
1. 125
2. 115.2
3. 105.2
4. 64

Answer 1

Correct Answer - Option 2 : 115.2

Given:

BC = 8 cm

DE = 5 cm

Area of ΔADE = 45 cm

Formula used:

ΔADE/ΔABC = (DE/BC)²

Calculation:

According to the question

⇒ ΔADE/ΔABC = (DE/BC)2

⇒ 45/ΔABC = (5/8)²

⇒ 45/ΔABC = 25/64

⇒ ΔABC = (45 × 64)/25

⇒ ΔABC = (2880/25)

⇒ ΔABC = 115.2 cm²

∴ The area of ΔABC is 115.2