Question

In the isosceles trapezoid ABCD shown with midsegment EF, if base BC = 22x, base AD = 17x + 12, and EF = 18.5x + 8, what is BC?

1) 22
2) 37
3) 44
4) 58

Answer 1

To find the value of base BC, we used the relationship between the bases and the midsegment of an isosceles trapezoid. By solving the equation derived from the midsegment length, we find BC to be 44.

This correct answer is 3)

Step-by-step explanation:

The student is asking for the length of base BC in an isosceles trapezoid ABCD given that base BC is equal to 22x, base AD is 17x + 12, and the midsegment EF is 18.5x + 8.

In an isosceles trapezoid, the midsegment length is the average of the lengths of the two bases, hence we can set up the equation (BC + AD) / 2 = EF using the given values.

Substituting with the given expressions, we have (22x + 17x + 12) / 2 = 18.5x + 8. To find the value of x, we first simplify the equation: 39x + 12 = 37x + 16. Then we solve for x: x = 2. Substituting x back into the expression for BC, we get BC = 22x and so BC = 22 * 2 = 44.

Therefore, the length of base BC is 44.

This correct answer is 3)