Question

The length of a rectangle is three times its width. The perimeter of the rectangle is at most 112 cm. Which inequality models the relationship between the width and the perimeter of the rectangle?
2w+2⋅(3w)≥112

2w+2⋅(3w)<112

2w+2⋅(3w)>112

2w+2⋅(3w)≤112

Answer 1

It's D (the one on the bottom)

Answer 2

Let

L--------> the length of the rectangle

W------> the width of the rectangle

we know that

the perimeter of rectangle is equal to

$P=2L+2W$

$P\leq112$

so

$2L+2W\leq112$ ---------> equation $1$

$L=3W$ -------> equation $2$

substitute equation $2$ in equation $1$

$2*[3W]+2W\leq112$

$6W+2W\leq112$

$8W\leq112$

$W\leq14\ cm$

therefore

the answer is the option

2w+2⋅(3w)≤112