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?
The perimeter of a trapezoid is the sum of all its sides. Therefore, we have:
9a + (5a + 1) + (17a - 6) + x = 39a - 7
Combining like terms:
31a - 5 + x = 39a - 7
Subtracting 31a from both sides:
x - 5 = 8a - 7
Adding 7 to both sides:
x = 8a + 2
Therefore, the length of the fourth side is 8a + 2.