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.

Answer 1

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.