SOLUTION: 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?

Algebra ->  Functions -> SOLUTION: 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?      Log On


   

Question 1125026: 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?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The formula for the perimeter of a trapezoid is
P=base%5B1%5D+%2B+base+%5B2%5D+%2B+side%5B+a%5D+%2B+side%5B+b%5D
given:
P=39a+-7 Three sides have the following
lengths:
side%5B+a%5D=9a, -> since trapezoid,
base+%5B2%5D=5a+%2B+1, and
base+%5B1%5D=17a+-+6
39a+-7=17a+-+6%2B+5a+%2B+1%2B+9a+%2B+side%5B+b%5D

39a+-7-17a+%2B6-5a+-+1-+9a+=+side%5B+b%5D
side%5B+b%5D=highlight%288a+-2+%29->the length of the fourth side
check:
plug it in
P=base%5B1%5D+%2B+base+%5B2%5D+%2B+side%5B+a%5D+%2B+side%5B+b%5D
39a+-7=%2817a+-+6%29%2B+%285a+%2B+1%29+%2B+9a%2B+%288a+-2%29
39a+-7=17a+-+6%2B+5a+%2B+1%2B+9a%2B+8a+-2
39a+-7=39a+-+7-> which confirms our solution