In the given figure, ∠PSR = 90°, PQ = 10 cm, QS = 6 cm and RQ = 9 cm, calculate the length of PR.
Pythagoras Theorem
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Question

In the given figure, ∠PSR = 90°, PQ = 10 cm, QS = 6 cm and RQ = 9 cm, calculate the length of PR.

KnowledgeBoat · Accepted Answer

In right angled triangle PQS,

By Pythagoras theorem,

Hypotenuse² = Perpendicular² + Base²

⇒ PQ² = PS² + QS²

⇒ 10² = PS² + 6²

⇒ 100 = PS² + 36

⇒ PS² = 100 - 36

⇒ PS² = 64

⇒ PS = $\sqrt{64}$

⇒ PS = 8 cm.

From figure,

RS = RQ + QS = 9 + 6 = 15 cm

In right angled △ PRS,

Hypotenuse² = Perpendicular² + Base²

⇒ PR² = RS² + PS²

⇒ PR² = 15² + 8²

⇒ PR² = 225 + 64

⇒ PR² = 289

⇒ PR = $\sqrt{289}$

⇒ PR = 17 cm.

Hence, the length of PR = 17 cm.

Mathematics