perplexus.info :: Shapes : Trapezoid Length Trial

Trapezoid Length Trial (Posted on 2016-02-21)

PQRS is a trapezoid with QR || PS.
It is known that:
QR = 1000, PS = 2008, and:
∠SPQ = 37^o, ∠PSR = 53^o
Points M and N are the respective midpoints of sides QR and PS

Find the length of MN.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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Solution

Comment 1 of 1

Extend PQ and RS to meet at T. Angle QTR (which is the same as angle PTS) is a right angle. Then triangles QTR and PTS are similar triangles.

T also lies on the line containing MN. That line is the median of angle QTR/PTS. The median from a right angle is congruent to half of the hypotenuse. Then TM = QR/2 = 500 and TN = PS/2 = 1004. Then MN = TN - TM = 504.

Posted by Brian Smith on 2016-02-21 14:09:24

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