Question

The length of a rectangle is five times its width. The perimeter of the rectangle is at most 96 cm.

Which inequality models the relationship between the width and the perimeter of the rectangle?

2w+2⋅(5w)>96

2w+2⋅(5w)<96

2w+2⋅(5w)≤96

2w+2⋅(5w)≥96

Answer 1

I think it's 3 one not sure lol sorry if I'm wrong

Answer 2

The right answer is the third option:
`2w+2(5w)\leq 96`

Explanation:

The perimeter is the length of the sides of the rectangle.

`perimeter=(2*width)+(2*lenght)`

`perimeter=2*w+2*l` (equation 1)

We've been told that in this case, the length of the rectangle is five times its width. So:

`l=5w`

Replacing in equation 1:

`perimeter=2w+2*(5w)`

Finally, we've been told that the perimeter of the rectangle is at most 96cm, this means that it may be 96cm or any quantity less than 96cm. This es represented with the symbol “less than or equal to” (
`\leq`), like this:

perimeter is less than or equal to 96cm

`perimeter\leq 96cm`

`2w+2(5w)\leq 96`

So, the right answer is the third option:
`2w+2(5w)\leq 96`