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Question

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

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Solution

(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.


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