F.2 Maths ---- Converse of Pyth. Theorem

An altitude AE of TriangeABC divides the side BC into 2 portions of the lengths 27cm and 48cm, put
BE = 27 cm
EC = 48 cm
As AE is an altitude of △ABC, in △ABE,
AB² = BE² + AE²
AB² = 27² + 36²
AB² = 2025

and in△AEC,
AC² = EC² + AE²
AC² = 48² + 36²
AC² = 3600

if △ABC is a right-angled triangle, AB² + AC² = BC²
AB² + AC² = 2025 + 3600 = 5625
BC² = (BE + EC)² = (27 + 48)² = 5625
AB² + AC² = BC², therefore, △ABC is a right-angled triangle