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.

viola Aug 19, 2020

#3**+2 **

**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**

Dragan Aug 21, 2020