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, the lengths of its legs (AB and CD) are equal.

Therefore, we can set up the following equation: 10y-16 = 8y-4.

To solve for y, we can subtract 8y from both sides of the equation to isolate the terms with y: 10y-8y-16 = 8y-8y-4.

Simplifying, we have 2y-16 = -4.

Next, we can add 16 to both sides of the equation to isolate the term with y: 2y-16+16 = -4+16.

Simplifying further, we get 2y = 12.

Finally, we can divide both sides of the equation by 2 to solve for y: 2y/2 = 12/2.

The solution is y = 6.