In triangle PQR,point S is the midpoint of side QR. If PQ=11,PR=17,PS=13, find QR
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Answer:
QR = 12
Step-by-step explanation:
In triangle PQR, point S is the midpoint of point of side QR.
QS = SR = 1/2 QR
PQ² + PR² = 2PS² + 2QS².......(by Appollonius theorem)
=> 11² + 17² = 2(13)² + 2QS²
=> 121 + 289 = 2(169) + 2QS²
=> 410 = 338 + 2QS²
=> 2QS² = 410 - 338
=> 2QS² = 72
=> QS² = 36
=> QS = 6
∴ QR = 2 × QS
∴ QR = 2 × 6
∴ QR = 12
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