ABCD is an isosceles trapezoid with legs AB and CD and base BC', If the length of AB = 10y-16, the length of BC' = 4у-6 and the length of CD =8y-4, find the value of y. Make sure to show ALL of your work in order to receive full credit.
Since ABCD is an isosceles trapezoid, the lengths of its legs AB and CD are equal. Therefore, we can set the lengths of AB and CD equal to each other and solve for y:
10y-16 = 8y-4
Rearranging the equation, we have:
10y - 8y = -4 + 16
2y = 12
Dividing both sides by 2, we get:
y = 6
Therefore, the value of y is 6.