The perimeter of a trapezoid is 39a - 7. Three sides have the following lengths: 9a, 5a + 1, and 17a - 6. What is the length of the fourth side?
a. 12
b. a - 7
b. 8a -2
d. 31a - 5
The perimeter of a trapezoid is the sum of the lengths of all its sides.
Given that the perimeter is 39a - 7 and that three sides have lengths 9a, 5a + 1, and 17a - 6, we can set up the following equation:
39a - 7 = 9a + 5a + 1 + 17a - 6
Simplifying the equation:
39a - 7 = 31a - 5
Subtracting 31a from both sides:
8a - 7 = -5
Adding 7 to both sides:
8a = 2
Dividing both sides by 8:
a = 1/4
So the length of the fourth side is:
9a + 5a + 1 + 17a - 6 = 9(1/4) + 5(1/4) + 1 + 17(1/4) - 6 = 9/4 + 5/4 + 1 + 17/4 - 6 = 11/4 + 17/4 - 6 = 28/4 - 6 = 7 - 6 = 1
Therefore, the length of the fourth side is 1.
The correct answer is:
a. 12