m∠B = 90 in ΔABC. is altitude to .

If AB = √10, AM = 2.5, find MC.

AB =

AM = 2.5

Applying Pythagoras theorem in ΔABM

AB² = AM² + BM²

⇒ BM² = 10 – 6.25 = 3.75

Let CM = x

AC = x + 2.5

Applying Pythagoras theorem in ΔCBM

⇒ BC² = BM² + CM²

⇒ BC² = x² + 3.75 …Equation (i)

Applying Pythagoras theorem in ΔABC

AC² = AB² + BC²

(x + 2.5)² = BC² + 10

⇒ x² + 6.25 + 5x = BC² + 10

⇒ BC² = x² – 3.75 + 5x …Equation (ii)

Equating Equation (i) and Equation (ii)

x² + 3.75 = x² – 3.75 + 5x

⇒ 5x = 7.5

⇒ x = 1.5

So CM = 1.5