Chapter 3.2, Problem 56E

To determine

To calculate : the length and width of the rectangle and write its equation for the perimeterod the rectangle in terms of $w$ .When the length of a rectangle is $5$ feet less than twice its width and the perimeter of rectangle is $38$ feet.

Answer to Problem 56E

The value of the expression is $w=8$ and $length=11$

Explanation of Solution

Given information : Consider, the value of the expression provided in the question

  $\begin{array}{l}width=w\\ length=2w-5\end{array}$

Formula used : $Perimeter=2\left(length+width\right)$

Calculation : To evaluate the expression it is needed to substitute the values in the above formula

  $Perimeter=2\left(length+width\right)$

  $38=2\left(2w-5+w\right)$

  $38=2\left(3w-5\right)$

Divide both sides of the equation with $2$ to isolate the variable term

  $\frac{38}{2}=\frac{2\left(3w-5\right)}{2}$

  $3w-5=19$

Add $5$ to both side of the equation to isolate the variable term

  $3w-5+5=19+5$

  $3w=24$

Divide both sides by $3$

  $\frac{3w}{3}=\frac{24}{3}$

  $w=8$

Then, the length of the rectangle is

  $length=2\left(8\right)-5=11$