5, 12, 13 are the lengths of the sides of a triangle. Show that the triangle is right angled. Find the length of altitude on the hypotenuse.

Hypotenuse (AB) = 13

Perpendicular (AC) = 12

Base (BC) = 5

∴ AC² + BC² = 5² + 12²

⇒ AC² + BC² = 25 + 144

⇒ AC² + BC² = 169 = AB²

Hence Pythagoras theorem is valid

m∠C = 90

Let AD = x, BD = 13 – x

Applying Pythagoras theorem

∴ Altitude CD² = 12² – x² = 5² – (13 – x) ²

⇒ 144 – x² = 25 – 169 – x² + 26x

⇒ 26x = 288

⇒ x = 11.07 units

So Altitude CD = √21.43 = 4.63 units