Question

2) In APQR, Point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR.
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Answer 1

QR = 12

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Answer 2

Step-by-step explanation:

In ∆PQR, point S is the midpoint of side QR. [Given]

∴ seg PS is the median.

∴ PQ2 + PR2 = 2 PS2 + 2 SR2 [Apollonius theorem}

∴ 112 + 172 = 2 (13)2 + 2 SR2

∴ 121 + 289 = 2 (169)+ 2 SR2 ∴ 410 = 338+ 2 SR2

∴ 2 SR2 = 410 – 338

∴ 2 SR2 = 72 ∴ SR2 = 72/2 = 36

∴ SR = √ 36 36 [Taking square root of both sides] = 6 units Now, QR = 2 SR [S is the midpoint of QR] = 2 × 6 ∴ QR = 12 units