Question

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In ∆ PQR, seg PM is the median, PM = 9 and PQ^2 + PR^2 =290. Find the length of QR.

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Answer 1

Answer:

• QR = 16 cm.

Step-by-step explanation:

Given:

• In ΔPQR, seg. PM is the median.
• PM = 9 cm
• PQ² + PR² = 290

To Find:

• QR.

Now, it is given that in ΔPQR, seg. PM is the median. So, by using Apollonius  Theorem.

⇒ PQ² + PR² = 2PM² + 2MR²

⇒ 290 = 2 × 9² + 2MR²

⇒ 290 = 162 + 2MR²

⇒ 128 = 2MR²

⇒ MR² = 64

⇒ MR = √64

⇒ MR = ±8 cm

But we know that side can't be negative. So,

∴ MR = 8 cm

Now, We know that,

⇒ QR = 2MR

⇒ QR = 2 × 8

⇒ QR = 16 cm.

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