ABCD is an isosceles trapezoid with legs AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ and base BC¯¯¯¯¯¯¯¯ , If the length of AB¯¯¯¯¯¯¯¯ =10y-16, the length of BC¯¯¯¯¯¯¯¯ = 4y-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. (2 points)
Since ABCD is an isosceles trapezoid, we know that AB is parallel to CD. Therefore, AB and CD must be of equal length.
Given that AB = 10y - 16 and CD = 8y - 4, we can set up the equation:
10y - 16 = 8y - 4
Simplifying the equation, we get:
2y = 12
Dividing both sides by 2, we find:
y = 6
Therefore, the value of y is 6.