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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.

Dec 30, 2022

#1
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The area of triangle PQR is 3*sqrt(13).

Dec 30, 2022
#2
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Because QN is a perpendicular midpoint, it is basically an altitude

We also know the base is 14, so the area of the triangle is $$12 \times 14 \div 2 = \color{brown}\boxed{84}$$

Dec 30, 2022