Question

Zach is creating a rectangular garden in his back yard. The length of the garden is 14feet. The perimeter of the garden must be at least 62 feet and no more than 94 feet.The width of the garden must be at least ---------feet and no more than---------- feet.

Answer 1

From the information provided, the length of the rectangular garden is 14 feet. The perimeter however is a compound inequality, that is, its value is a range between 62 ft and 94 ft. That is;

`\begin{gathered} \text{Where p}=perimeter, \\ 62\le p\le94 \end{gathered}`

We shall take the values at both ends of this interval and solve as follows;

`\begin{gathered} \text{Perimeter of a rectangle;} \\ P=2l+2w \\ \text{When the perimeter is 62, and the length is 14;} \\ 2(14)+2w\ge62 \\ 28+2w\ge62 \\ \text{Subtract 28 from both sides;} \\ 2w\ge34 \\ \text{Divide both sides by 2} \\ w\ge17 \end{gathered}`

This means the width of the garden must be at least 17 feet.

Also, we would have;

`\begin{gathered} \text{When the perimeter is 94 and the length is 14;} \\ 2l+2w\le94 \\ 2(14)+2w\le94 \\ 28+2w\le94 \\ \text{Subtract 28 from both sides;} \\ 2w\le66 \\ \text{Divide both sides by 2;} \\ w\le33 \end{gathered}`

This means the width is no more than 33 feet

Therefore our range of values for the width are;

ANSWER:

`\begin{gathered} \text{The width of the garden must be at least 17ft} \\ w\ge17 \\ And\text{ no more than 33 ft} \\ w\le33 \end{gathered}`