The length of the isosceles trapezoid AC = 29, BD = 29, and CD = 45.
Calculating the sides of an isosceles trapezoid.
In an isosceles trapezoid ABCD, the diagonals are congruent. Thus, the length of the parallel sides AC and BD are congruent.
From the given information;
AC = 7x - 6
BD = 4x + 9
CD = 12x - 15
Since AC and BD are congruent
AC = BD
7x - 6 = 4x + 9
Collect like terms
7x - 4x = 9 + 6
3x = 15
x = 15/3
x = 5
Now, that x is know:
AC = 7x - 6
AC = 7(5) - 6
AC = 35 - 6
AC = BD = 29
CD = 12x - 15
CD = 12(5) - 15
CD = 60 - 15
CD = 45