Chapter 4.2, Problem 46HP

To determine

To explain: an equation in standard form that models all possible combinations of lengths and widths for a rectangle having a perimeter of 100 meters by taking five cases.

Explanation of Solution

Perimeter of the rectangle should be 100 meters.

Now, perimeter of rectangle is given by

  $P=2\left(x+y\right)$

Where x and y are the length and width respectively.

Now, for perimeter to be 100, the sum of length and width should be

  $\begin{array}{c}\left(x+y\right)=\frac{100}{2}\\ =50\end{array}$

Now, take some natural numbers whose sum will give 50.

x	25	24	23	24	1
y	25	26	27	26	49

So, the model equation will be

  $P=A_x+B_y$