Question

The perimeter of a rectangle is to be between 140 and 220 inches. FindThe range of values for its length when its width is 20 inches

Answer 1

The lower value of the perimeter is 140 inches .

Width of the rectangle is 20 inches .

The length of the rectangle is calculated as ,

`\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 140=\text{ 2 ( Length + }20\text{ )} \end{gathered}`

Rearranging the terms ,

`\begin{gathered} \text{Length + 20 = }(140)/(2) \\ \text{Length + 20 = 70} \\ \text{Length = 50 inches} \end{gathered}`

The higher value of perimeter is 220 inches .

Width of the rectangle is 20 inches .

The length is calculated as,

`\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 220=\text{ 2 ( Length + }20\text{ )} \end{gathered}`

Therefore,

`\begin{gathered} \text{Length + 20 = 110} \\ \text{Length = 110 - 20} \\ \text{Length = 90 inches} \end{gathered}`

Thus the range of values for the length of the given rectangle are 50 and 90 .