Question

Dylan is creating a rectangular garden in his back yard. The length of the garden is 16 feet. The perimeter of the garden must be at least 68 feet and no more than 100 feet.The width of the garden must be at least feet and no more than feet.

Answer 1

We can write the range for w as : 18 ≤ w ≤ 34

Explanation:

The perimeter of rectangle is given as :

P = 2 ( length + width)

or P = 2 l + 2 w

Now, given the length of the garden is 16 feet

Also given is that the perimeter of the garden must be at least 68 feet and no more than 100 feet.

So, this can be written as :

`68 \leq P \leq 100`

or,
`68 \leq (2l + 2w) \leq 100`

Substitute l = 16, we get:

`68 \leq (2(16) + 2w) \leq 100`

`68 \leq (32 + 2w) \leq 100\\\implies 68 - 32\leq 2w \leq 100-32\\\implies 36\leq 2w \leq 68\\\implies 18\leq w \leq 34`

So, we can write the range for w as : 18 ≤ w ≤ 34