Question

Isosceles trapezbid ABCD is shown with midsegment EF. If base BC=17x, base AD=30x+12, and EF=22.5x+9, what is BC ?

a) 34
b) 51
c) 68
d) 85

Answer 1

The midsegment of an isosceles trapezoid is the average of the bases. By setting the formula for the midsegment equal to the given expression, we can solve for x and find the value of BC.

Step-by-step explanation:

The formula for the midsegment of an isosceles trapezoid is the average of the bases. In this case, the midsegment EF is equal to (BC + AD) / 2. We are given that EF = 22.5x + 9, BC = 17x, and AD = 30x + 12. Substituting these values into the formula, we get (17x + 30x + 12) / 2 = 22.5x + 9.

Now, we can solve for x. Simplifying the equation, we get 47x + 12 = 45x + 18. Subtracting 45x from both sides, we get 2x + 12 = 18. Subtracting 12 from both sides, we get 2x = 6. Dividing both sides by 2, we get x = 3.

Finally, we can substitute x = 3 back into the equation for BC to find its value. BC = 17(3) = 51. Therefore, the answer is b) 51.