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Trapezoid PQRS has bases PQ and RS. The median MN meets the diagonals PR and QS at A and B, respectively. If SR=20 and AB=7, find PQ.

 May 8, 2020
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Since MN is a median of the trapezoid, MA will be the middle line of triangle(PRS) and equal to one-half the base.

This makes MA = 10.

Also BN will be the middle line of triangle(QRS) and equal to 10.

MA + BN  =  10 + 10  =  20; but they have an overlap of 7   --->   MN  =  13.

13 is one-half the sum of the two bases; since one base is 20, the other base must be 6.

 May 9, 2020

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