Question

The sides of similar triangles ΔMNO and ΔDEF are in the ratio 4 ∶ 7. If area of ΔMNO is equal to 128 cm², what is the area of ΔDEF? 
1. 400 cm²
2. 392 cm²
3. 360 cm²
4. 358 cm²

Answer 1

Correct Answer - Option 2 : 392 cm²

Given:

ΔMNO ∼ ΔDEF

The sides of ΔMNO and ΔDEF are in the ratio 4 ∶ 7.

Area of (ΔMNO) = 128 cm²

Concepts used:

The ratio of the area of similar triangles is equal to the square of the ratio of sides of corresponding triangles.

Calculation:

ΔMNO ∼ ΔDEF

Area (ΔMNO)/Area (ΔDEF) = (Side of ΔMNO/Side of ΔDEF)²

⇒ 128 cm²/Area (ΔDEF) = (4/7)²

⇒ Area (ΔDEF) = 128 × (49/16) cm²

⇒ Area(ΔDEF) = 392 cm².

∴ Area of ΔDEF is equal to 392 cm².