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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

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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.

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