Chapter 12, Problem 41CR

To determine

To find: The length of the next longest side of the hexagon with longest side 7 where the sides are in AP.

Answer to Problem 41CR

The length of the next longest side measures 6.2

Explanation of Solution

Given Information:

Longest side of the hexagon $\left(l\right)=7$

Perimeter of the hexagon $\left(P\right)=30$

Formula used:

Terms of an A.P. are $a,a+d,a+2d,a+3d,\mathrm{....}$

  $"a"$ is the first term

  $"d"$ is the common difference

Calculation:

Let the difference between each consecutive pair be $d$

As 7 is the longest side, so the other sides will decrease by a constant number $d$

Therefore, the other six sides of the hexagon will be $7-d,7-2d,7-3d,7-4d\text{and}7-5d$

As the perimeter of the hexagon is $P=30$

  $\begin{array}{l}\therefore 7+7-d+7-2d+7-3d+7-4d+7-5d=30\\ \therefore 42-15d=30\\ \therefore 15d=12\\ \therefore d=0.8\end{array}$

So, the next longest side is $7-d=7-0.8=6.2$

Hence, the length of the next longest side measures 6.2.