Question

Two similar triangles - ΔMNO and ΔMNP are drawn between two opposite lines with the same base MN. If the ratio of the perimeter of ΔMNO and ΔMNP is x ∶ y and NO is equal to x², what is the value of side NP? 
1. xy
2. y²
3. x/y
4. None of these

Answer 1

Correct Answer - Option 1 : xy

Given:

ΔMNO ∼ ΔMNP

The perimeter of ΔMNO ∶ Perimeter of ΔMNP = x ∶ y

NO = x² 

Concepts used:

The ratio of corresponding sides of similar triangles and the ratio of the perimeter of similar triangles are equal.

Calculation:

ΔMNO ∼ ΔMNP

⇒ Perimeter of ΔMNO/Perimeter of ΔMNP = NO/NP

⇒ Perimeter of ΔMNO/Perimeter of ΔMNP = x ∶ y

⇒ NO/NP = x ∶ y

⇒ x²/NP = x/y

⇒ NP = (x² × y)/x

⇒ NP = xy cm.

∴ The value of side NP is xy.