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Question
PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.
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Solution
Since, PQR is an isosceles triangle and PS ⊥ QR,
therefore it divides QR into two equal parts.
In ΔPSQ, ∠S = 90°
∴ PQ2 = PS2 + QS2 ....(By Pythagoras Theorem)
⇒ PS2 = PQ2 - QS2
= 102 - 62
= 100 - 36
= 64
⇒ PS = 8cm.
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