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.

1 answer

Since ABCD is an isosceles trapezoid, legs AB and CD have the same length.

Therefore, we have the equation:

10y - 16 = 8y - 4

Simplifying the equation, we get:

2y = 12

Dividing both sides by 2, we get:

y = 6

Therefore, the value of y is 6.