Question

PLEASE HELP ME!!!

Answer 1

Answer:

Part a) The inequality that models this problem is $2w+2(4w) \leq 106$

Part b) The greatest possible value for the width is 10.6 centimeters

Step-by-step explanation:

Part a) Which inequality models this problem?

Let

l ----> the length of the rectangle in cm

w ---> the width of the rectangle in cm

we know that

The perimeter  of the rectangle is equal to

$P=2w+2l$

Remember that

The term "at most" means "less than or equal to"

so

$2w+2l \leq 106$ ----> inequality A

$l=4w$ ---> equation B

substitute equation B in the inequality A

$2w+2(4w) \leq 106$ ---> inequality that model the problem

Part b) what is the greatest possible value for the width?

solve for w

$2w+2(4w) \leq 106$

$10w \leq 106$

Divide by 10 both sides

$w \leq 10.6\ cm$

therefore

The greatest possible value for the width is 10.6 centimeters