Given:

klmn is a trapezoid, kl=mn,

ab is a midsegment, ab=18,

kl=15, lm: kn=1: 5

find the height.

9 units

Step-by-step explanation:

By the midsegment theorem,

Since the ratio then and

Draw two heights LE and MF. Quadrilateral ELMF is a rectangle, then EF = LM = 6 units.

Trapezoid KLMN is isosceles trapezoid (KL = MN), then KE = FN and

Consider right triangle KLE. By the Pythagorean theorem,

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

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