Question

In the given figure. PQ = PS, P =R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.

Answer 1

In ΔSRQ, ∠R = 90°
∴ QS² = RS² + QR²     ....(Pythagoras Theorem)
= 20² + 21²
= 440 + 441
= 841
Now,
In ΔQSP, ∠P = 90°
∴ QS² = PQ² + PS²
⇒ QS² = PQ² + PQ²     ....(Pythagoras Theorem)
⇒ QS² = 2PQ²              ....(Given PQ = PS)

⇒ PQ2 = `"QS"^2/(2) = (841)/(2)` = 420.5
⇒ PQ = 20.50cm.