Question

Isosceles trapezoid ABCD is shown with midsegment EF. If base BC = 15x, base AD = 32x − 2, and EF = 20.5x + 8, what is BC?

Answer 1

The value of the length of BC is 45 units

How to determine the length BC?

The given parameters are:

BC = 15x

AD = 32x - 2

EF = 20.5x + 8

Where the parallel bases are AD and BC and the midsegment is EF

By the midsegment theorem, we have

2 * EF = AD + BC

Substitute the known values in the above equation

2 * (20.5x + 8) = 15x + 32x -2

Open the bracket

41x + 16 = 15x + 32x - 2

Evaluate the like terms

6x = 18

Divide both sides by 6

x = 3

Substitute x = 3 in BC = 15x

BC = 15 * 3

Evaluate

BC = 45

Hence, the value of the length of BC is 45 units

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