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?
To find the length of the fourth side of the trapezoid, we need to add up the lengths of all four sides and set it equal to the given perimeter.
The three given sides are:
9a, 5a + 1, and 17a - 6
Let the length of the fourth side be x.
So, the equation becomes:
9a + (5a + 1) + (17a - 6) + x = 39a - 7
Combine like terms:
31a - 5 + x = 39a - 7
Subtract 31a from both sides:
-5 + x = 8a - 7
Add 5 to both sides:
x = 8a - 2
Therefore, the length of the fourth side is 8a - 2.