Isosceles trapezoid ABCD is shown with midsegment EF. If base BC = 17x, base AD = 30x + 12, and EF = 22.5x + 9, what is BC?
Isosceles trapezoid A B C D is drawn with parallel bases A D and B C and midsegment E F.
34
51
68
85
To find the length of base BC, we can set up an equation using the properties of isosceles trapezoids and midsegments.
Since EF is a midsegment, it is equal to the average of the lengths of the bases: EF = (BC + AD)/2.
Substitute the given values:
22.5x + 9 = (17x + 30x + 12)/2
22.5x + 9 = 23.5x + 6
3 = 1x
x = 3
Now, we can find the length of base BC:
BC = 17x
BC = 17(3)
BC = 51
Therefore, base BC is 51 units long. The answer is 51.