Question

In ∆KLM, l (KL) = 9 cm, l (LM) = 12 cm and l (KM) = 15 cm. Is ∆KLM a right-angled triangle? If it is, name the angle that measures 90°.

Answer 1

Given, in ∆KLM, l(KL) = 9 cm, l(LM) = 12 cm and l(KM) = 15 cm.
Longest side = l(KM) = 15 cm
Square of longest side = (KM)² = (15)² = 225
One side = l(KL) = 9 cm
Square of one side = (KL)² = (9)² = 81
Other side = l(LM) = 12 cm
Square of other side = (LM)² = (12)² = 144
Consider (KL)² + (LM)² = 81 + 144 = 225
= (KM)²
Hence, ∆KLM is a right-angled triangle.


Since, the longest side of a right-angled triangle is the hypotenuse,
KM is the hypotenuse.
Also, angle opposite to the hypotenuse is the right angle.
∴ $\angle$L is 90^o