Chapter 8.1, Problem 42PPE

To determine

To find:The length of the fourth side of the trapezoid.

Answer to Problem 42PPE

  $8a-2$

Explanation of Solution

Given information:The perimeter of a trapezoid is $39a-7$ . Three sides have the lengths $9a,5a+1,\text{ and }17a-6$ .

Calculation:

Let the length of the fourth side be x.

According to the problem,

  $\begin{array}{l}9a+(5a+1)+(17a-6)+x=39a-7\\ \Rightarrow 9a+5a+1+17a-6+x=39a-7\\ \Rightarrow (9a+5a+17a)+(1-6)+x=39a-7[\text{combining like terms]}\\ \Rightarrow 31a-5+x=39a-7\\ \Rightarrow x=39a-7-(31a-5)\\ \Rightarrow x=39a-7-31a+5\\ \Rightarrow x=(39a-31a)+(-7+5)[\text{combining like terms]}\\ \Rightarrow x=8a-2\end{array}$

Thus, the fourth side is $8a-2$ .