Chapter 13.5, Problem 42SR

To determine

To determine number of possible outcomes for given situation.

Answer to Problem 42SR

Total possible outcomes for given situation is 3.

Explanation of Solution

Given information:

Perimeter of rectangle is 12, with side lengths as integers.

We know perimeter of rectangle is $2\left(a+b\right)$ where $a,b$ are the sides of rectangle.

Therefore,

  $\begin{array}{l}2\left(l+b\right)=12\\ l+b=6\end{array}$

Hence the ways in which the sum of two sides is 6 are,

(1+5), (2+4), (3+3)

Therefore there are only three ways.