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$In $\triangle PQR$, we have $PQ = QR = 34$ and $PR = 32$. Find the length of median $\overline{QM}$.$

Guest Nov 16, 2014

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Best Answer

The median would bisect side PR. And angle QMR is right....so...by the Pythagorean Theorem, we have...

√[QR² - MR²] = √[34² - 16²] = √[1156 - 256] = √900 = 30 = QM

CPhill Nov 16, 2014

CPhill · Answer 1 · 2014-11-16T04:23:37

The median would bisect side PR. And angle QMR is right....so...by the Pythagorean Theorem, we have...

√[QR² - MR²] = √[34² - 16²] = √[1156 - 256] = √900 = 30 = QM

Alan · Answer 2 · 2014-11-16T04:14:56

This is an isosceles triangle, so the triangle formed by PQM is a right-angled triangle with PQ = 34, PM = 16, so QM = √(34² - 16²)

$${\mathtt{QM}} = {\sqrt{{{\mathtt{34}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{16}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{QM}} = {\mathtt{30}}$$

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Edited: corrected to get signs right!

Alan · Answer 3 · 2014-11-16T04:41:53

Oops! Got sign wrong. Thanks to Chris, I've now noticed this and corrected it.

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