Question

In ΔMNP,∠MNP =90, segNQ⊥segMP,  MQ=9  , QP=4,  then NQ=---------.

 a)6

 b)5

 c)7

 d)8

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Answer 1

Answer:

6.

Step-by-step explanation:

Let MN = a and NP = b.

And NQ = x.

Then in triangle MNQ,  $a^{2} =x^{2}+9 ^ {2}$   ------------------------(1)

In triangle NQP,  $b^{2}=x^{2}+4^{2}$   ------------------------(2)

In triangle MNP,  $a^{2}+b^{2}=(13)^{2}$    -----------------------(3)

(1)+(2)  =>  $a^{2} +b^{2}=2x^{2}+97$

           =>  $169=2x^{2}+97$       [From (3)]

           =>  $x^{2}=36$

           =>  x = 6.

Therefore, NQ = x = 6.