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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°

∴ PQ^{2} = PS^{2 }+ QS^{2} ....(By Pythagoras Theorem)

⇒ PS^{2} = PQ^{2} - QS^{2}

= 10^{2} - 6^{2}

= 100 - 36

= 64

⇒ PS = 8cm.

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