The shorter side of a trapezoid is equal to its height, and the longer side is 3/2 times as long. if the area is 80, find the length of the shorter side.

  8

Step-by-step explanation:

Let s represent the length of the shorter base and height. Then (3/2)s is the length of the longer base.

The area formula for a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  80 = (1/2)(s +3/2s)s = 5/4s²

  64 = s² . . . . . . . . . . . . . . . . . . . multiply by 4/5

  8 = s . . . . . . . . . . . . . . . . . . . . . take the square root

The length of the shorter side is 8.

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