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# Geometry

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In triangle PQR, let M be the midpoint of QR, let N be the midpoint of PR, and let O be the intersection of QN and RM, as shown. If QN perp PR, QN = 12, and PR = 14, then find the area of triangle PQR.

Feb 8, 2023

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Because a side is perpendicular to a median, the triangle is isosceles.

Because $$PR = 14$$, and $$QN = 12$$, the area of the triangle is $$12 \times 14 \div 2 = \color{brown}\boxed{84}$$

Note that PR is a base and QN is the height.

Feb 8, 2023