Answer:
We can write the range for w as : ![19\leq w\leq 40](https://tex.z-dn.net/?f=19%5Cleq%20w%5Cleq%2040)
Step-by-step explanation:
The perimeter of rectangle is given as :
or ![P=2l+2w](https://tex.z-dn.net/?f=P%3D2l%2B2w)
Where l = length and w = width
Given is : the length of the garden is 16 feet
Also given is that the perimeter of the garden must be at least 70 feet and no more than 112 feet.
So, this can be shown as :
![70\leq P\leq 112](https://tex.z-dn.net/?f=70%5Cleq%20P%5Cleq%20112)
=> ![70\leq (2l+2w)\leq 112](https://tex.z-dn.net/?f=70%5Cleq%20%282l%2B2w%29%5Cleq%20112)
Putting l = 16
=> ![70\leq (2(16)+2w)\leq 112](https://tex.z-dn.net/?f=70%5Cleq%20%282%2816%29%2B2w%29%5Cleq%20112)
=> ![70\leq (32+2w)\leq 112](https://tex.z-dn.net/?f=70%5Cleq%20%2832%2B2w%29%5Cleq%20112)
=> ![70\leq (32+2w) \leq 112](https://tex.z-dn.net/?f=70%5Cleq%20%2832%2B2w%29%20%5Cleq%20112)
=>
and ![2w \leq 112-32](https://tex.z-dn.net/?f=2w%20%5Cleq%20112-32)
=>
and ![2w \leq 80](https://tex.z-dn.net/?f=2w%20%5Cleq%2080)
=>
and ![w \leq 40](https://tex.z-dn.net/?f=w%20%5Cleq%2040)
So, we can write the range for w as : ![19\leq w\leq 40](https://tex.z-dn.net/?f=19%5Cleq%20w%5Cleq%2040)