Question

XYZ is a right angled triangle with angle X=90,XY=9cm,and YZ=12cm. OX is perpendicular to YZ . find OX​

Answer 1

$\bold {OX= \frac{9\times \sqrt{7}}{4}\ cm}$

Step-by-step explanation:

Given,

∠X = 90°,YZ= 12 cm,XY =12 cm,OX⊥YZ

Now In ΔXYZ and ΔYOX

∠X = ∠XOY = 90°

∠Y = ∠Y [Common]

By AA similarity

ΔXYZ is similar to ΔYOX

∴, $\frac{YO}{YX} = \frac{OX}{XZ}= \frac{YX}{YZ}.$............(1)

Now,By Pythagoras Theorem,

$(XZ)^2 + (XY)^2 = (YZ)^2$

$(XZ)^2 + (9)^2 = (12)^2$

$(XZ)^2+ 81 = 144$

$(XZ)^2 = 144-81$

           = 63

XZ = √(63) cm

Now,From equation (1)

OX = $\frac{XZ\times YX}{YZ}$

     = $\frac{\sqrt{63}\times YX}{YZ}$

$\bold {OX= \frac{9\times \sqrt{7}}{4}\ cm}$