Chapter 11.1, Problem 14PSB

To determine

To find : The probability that each rectangle has a perimeter greater than $40$

Answer to Problem 14PSB

The probability is $P=\frac{2}{5}$

Explanation of Solution

Given information : The following information has been given

Area of the rectangles is $72$

Each rectangle has a perimeter greater than $40$

Formula used : The probability will be

  $P=\frac{F}{T}$

Where F is the favorable number of outcomes, and T is the total number of outcomes

Calculation : We know that if the area of the rectangles is $72$ , then their dimensions could be

  $(8,9),(1,72),(2,36),(4,18),(6,12),(24,3)$

Thus, we have a total of $12$ possible outcomes

Now, if each rectangle has a perimeter greater than $40$ , then our coordinates would be

  $(72,1),(2,36),(4,18),(3,24)$

Hence, our probability would be

  $\begin{array}{l}P=\frac{{}^4{C}_2}{{}^6{C}_2}\\ P=\frac{6}{15}\\ P=\frac{2}{5}\end{array}$