Question

In the given figure, O is a point inside a ΔMNP such that ∠MOP = 90°, OM = 16 cm and OP = 12 cm. If MN = 21 cm and ∠NMP = 90° then NP = ?

Options

• 25 cm

• 29 cm

• 33 cm

• 35 cm

Answer 1

29 cm

Explanation:

In right triangle MOP, OM = 16 and OP = 12 with ∠MOP = 90°.

So, `MP = sqrt(16^2 + 12^2)` 

= `sqrt(400)`

= 20 cm 

In triangle MNP, ∠NMP = 90°.

So, MN and MP are the legs; thus `NP = sqrt(MN^2 + MP^2)` 

= `sqrt(21^2 + 20^2)`

= `sqrt(441 + 400)`

= `sqrt(841)`

= 29 cm