Final answer:
To find the length of BD in the isosceles trapezoid BCDE, set up an equation and solve for x. Substitute the value of x back into the equation to find the length of BD.
Step-by-step explanation:
To find the length of BD in the isosceles trapezoid BCDE, we can set up an equation using the given information. BD is equal to 8x - 27 and EC is equal to 2x + 33. Since BCDE is an isosceles trapezoid, BD is equal to EC. So we can set up the equation 8x - 27 = 2x + 33 and solve for x.
8x - 27 = 2x + 33
6x = 60
x = 10
Now that we know the value of x, we can substitute it back into the equation to find the length of BD.
BD = 8(10) - 27
BD = 80 - 27
BD = 53
The length of BD is 53.