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
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.