Chapter 1, Problem 37RP

To determine

To calculate: Range of possible values of width of the rectangle have to be calculated

Answer to Problem 37RP

The following range of values for w have been found: $6<w<10$

Explanation of Solution

Given information: Let the width of the rectangle be w, and length be l.

  $Perimeter=20$

  $l<4$

Formula used: The following formulas have been used

  $Perimeter=2(l+w)$

  $Perimeter=20$

Calculation: We equate the values of perimeter from the above two equations :

  $20=2(l+w)$

So, we can say that

  $l=10-w$

Now, using the given information that $0<l<4(0<l$ because length can’t be negative) :

  $0<\left(10–w\right)<4$

Thus, solving for w we get

  $6<w<10$