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Quadrilateral PQRS is a trapezoid with bases PQ and RS. The median MN meets the diagonals PQ and RS at X and Y, respectively. If SR=20 and XY=7, find PQ.

 

 Aug 19, 2020
 #1
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PQ = 2*20 - 7 = 33.

 Aug 19, 2020
 #2
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I dont even know how you came up with that c**p

 Aug 19, 2020
 #3
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Quadrilateral PQRS is a trapezoid with bases PQ and RS. The median MN meets the diagonals PQ and RS at X and Y, respectively. If SR=20 and XY=7, find PQ.

 

Let's draw a vertical line that intersects point W on SR and point Z on PQ. Line WZ passes through point X.

 

Let the line segment WZ be 14 units.   (btw, that can be any positive value)

 

Find an angle XRW                ∠XRW = arctan(XW / XR) = 27.40757544º

 

PQ = 2[XZ / tan(∠XRW)] + XY = 34 units

 Aug 21, 2020
 #4
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This assumes that it's an isosceles trapezium, which needn't be the case.

Guest Aug 21, 2020

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