Question

) In XYZ, ∠X = 90⁰, XY = 24 cm, XZ = 70 cm. Seg XM is the median on the hypotenuse. Therefore XM = ? ​

Answer 1

Answer:

GIVEN :

In ∆XYZ right angled at X

XY=24cm

XZ=70cm

XM is a median on hypotenuse

⇒{ZM=MY}

SOLUTIONS :

By Pythagoras theorem to find hypotenuse

${zy}^{2} = {zx}^{2} + {xy}^{2}$

${zy}^{2} = {70}^{2} + {24}^{2}$

${zy}^{2} = 4900 + 576$

$zy = \sqrt{5476}$

$zy = 74$

Now length of the median of right angle

$xm = \frac{1}{2} \times zy$

$xm = \frac{1}{2} \times 74$

$xm = 37cm$

Hence the length of the median XM

⇒37cm