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, we need to subtract the sum of the lengths of the three given sides from the perimeter of the trapezoid.
The perimeter is given by the expression 39a – 7.
The sum of the three given sides is: 9a + (5a + 1) + (17a – 6).
Using the distributive property, we have 9a + 5a + 1 + 17a – 6.
Simplifying this expression, we get 31a – 5.
To find the length of the fourth side, we subtract this sum from the perimeter:
39a – 7 – (31a – 5).
Using the distributive property again, we have: 39a – 7 – 31a + 5.
Combining like terms, we get: 8a – 2.
Therefore, the length of the fourth side is 8a – 2.