ABCD is an isosceles trapezoid with legs AB¯¯¯¯¯¯¯¯AB¯ and CD¯¯¯¯¯¯¯¯CD¯ and base BC¯¯¯¯¯¯¯¯BC¯ , If the length of AB¯¯¯¯¯¯¯¯AB¯ =10y-16, the length of BC¯¯¯¯¯¯¯¯BC¯ = 4y-6 and the length of CD¯¯¯¯¯¯¯¯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, we know that AB = CD. Therefore, we can set up the equation:
10y - 16 = 8y - 4
Subtract 8y from both sides:
2y - 16 = -4
Add 16 to both sides:
2y = 12
Divide both sides by 2:
y = 6
Therefore, the value of y is 6.