Question

The perimeter of a square garden is to be at least 30 feet but not more than 64 feet. Find all possible values for the length of its sides.

Answer 1

`4x \in <30.64>/:4 \\ x \in <7.5,16>`

Answer 2

`7.5\leq x\leq 16`

Step-by-step explanation:

Let x be the length of each side of square.

Since the perimeter of the square is 4 times the length of each side, so perimeter of our given circle will be 4x.

We have been given that the perimeter of a square garden is to be at least 30 feet but not more than 64 feet.

This means the perimeter of the garden should we greater than or equal to 30 feet and less than or equal to 64 feet.

We can represent this information in an equation as:

`30\leq 4x\leq64`

Let us divide our inequality by 4 to solve for x.

`(30)/(4)\leq (4x)/(4)\leq(64)/(4)`

`7.5\leq x\leq 16`

We can represent our answer in interval notation as:
`[7.5,16]`

Therefore, the length of the square's side can be any number between 7.5 feet and 16 feet including both 7.5 and 16 as well.