Question

1) In figure, angleMNP = 90° seg NQ perpendicular seg MP, MQ = 9, QP = 4, find NQ. .​

Answer 1

$\small \bold{Area \: of \: ΔMPN= \frac{1}{2} (MN)(NP)= \frac{1}{2} (NQ)(MP)}$

∴(MN)(NP)=(NQ)(MP)

∴MP=9+4=13

$\bold{∴MN^2 +NP^2 =169}$

$\bold{∴MN^2 =81+NQ^2}$

$\bold{∴NP^2 =16+NQ^2}$

$\bold{ ∴81+16+2NQ^2 =169}$

$\bold{∴NQ^2 = \frac{169 - 97}{2} }$

$\bold{∴NQ^2 =36}$

∴NQ=6.