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.

Guest May 8, 2020

#1**0 **

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.

geno3141 May 9, 2020