Question

Some triangles are given below with the lengths of two sides specified. Can you find the length of the third side?

Answer 1

(i) The given triangle is

By Pythagoras’ Theorem, we have

(AB)² = (AC)² − (BC)²

⇒ (AB)² = (17 cm)² − (15 cm)²

⇒ (AB)² = (289 − 225) cm²

⇒ (AB)² = 64 cm²

⇒ AB =

⇒ AB = 8 cm

Thus, the length of the third side of the given right-angled triangle is 8 cm.

(ii) The given triangle is

By Pythagoras’ Theorem, we have

(AC)² = (AB)² + (BC)²

⇒ (AC)² = (12 cm)² + (5 cm)²

⇒ (AC)² = (144 + 25) cm²

⇒ (AC)² = 169 cm²

⇒ AC =

⇒ AC = 13 cm

Thus, the length of the third side of the given right-angled triangle is 13 cm.

(iii) The given triangle is

By Pythagoras’ Theorem, we have

(BC)² = (AC)² − (AB)²

⇒ (BC)² = (20.5 cm)² − (4.5 cm)²

⇒ (BC)² = (420.25 − 20.25) cm²

⇒ (BC)² = 400 cm²

⇒ BC =

⇒ BC = 20 cm

Thus, the length of the third side of the given right-angled triangle is 20 cm.