Question

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
C. 8a – 2
D.31a – 5

Answer 1

Answer: 8a-2

Step-by-step explanation:

The perimeter of a trapezoid is the addition of its four sides.

Perimeter of trapezoid= 39a – 7.

Length of 1st side= 9a,

Length of 2nd side= 5a + 1,

Length of third side= 17a – 6.

Length of the fourth side= Unknown

To find the length of the 4th side, we add the length of the three sides together and subtract from the perimeter of the trapezoid. This will be:

= 39a-7 - (9a+5a+1+17a-6)

= 39a-7-(9a+5a+17a+1-6)

= 39a-7-(31a-5)

=39a-7-31a+5

= 39a-31a-7+5

= 8a-2

The length of the 4th side is 8a-2

Answer 2

We know the perimeter is the total sum of all sides of the shape, we can use this to form an equation: the perimeter=1st side + 2nd side + 3rd side + 4th side 39a-7=9a+(5a+1)+(17a-6)+4th side.
Collect like terms to get 39a-7=31a-5+4th side
If we move everything but the 4th side over to the left we can solve 
C. 8a-2=4th side is the correct answer