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. (4 points)
Since ABCD is an isosceles trapezoid, the legs AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are congruent. Therefore, we can set their lengths equal to each other:
10y-16 = 8y-4
Subtracting 8y from both sides:
2y-16 = -4
Adding 16 to both sides:
2y = 12
Dividing by 2:
y = 6
Therefore, the value of y is 6.