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, its legs AB and CD are congruent. This means that 10y-16 = 8y-4.
Subtracting 8y from both sides:
10y - 8y - 16 = 8y - 8y - 4
2y - 16 = -4
Adding 16 to both sides:
2y - 16 + 16 = -4 + 16
2y = 12
Dividing both sides by 2:
2y/2 = 12/2
y = 6
Therefore, the value of y is 6.