Isosceles trapezoid ABCD is shown with midsegment EF. If base BC = 22x, base AD = 17x + 12, and EF = 18.5x + 8, what is BC?
Isosceles trapezoid A B C D is drawn with parallel bases A D and B C and midsegment E F.
22
37
44
58
To find the length of base BC, we first need to find the value of x.
Given that EF is the midsegment, we know that EF is equal to the average of base BC and base AD.
So, we have the equation:
EF = (BC + AD) / 2
Substitute the given values:
18.5x + 8 = (22x + 17x + 12) / 2
18.5x + 8 = 39.5x + 12
39.5x - 18.5x = 12 - 8
21x = 4
x = 4 / 21
Now we can find the length of base BC by substituting the value of x into the equation:
BC = 22x
BC = 22 * (4 / 21)
BC = 88 / 21
BC = 4.1905
Therefore, BC is approximately 4.19.