Inequality word problem. Helppp!

Question

A length of a rectangular fence of a garden is 3m more than the width. The perimeter of the garden cannot be more than 24m.

a) write down an inequality to show this

b)it is given that the area must be atleast 28m^2.

write down an inequality showing this.

c) hence, find the possible value for the width of the garden

Answer 1

P = 2(l + w)

A = lw

l = w + 3

a) This can be confusing, but to be no more than 24m, it must be less than or equal to 24

2(w + w + 3) ≤ 24

2(2w + 3) ≤ 24

2w + 3 ≤ 12

b) To be at least 28m², it has to be equal to or greater than 28.

w(w + 3) ≥ 28

w² + 3w ≥ 28

c) 2w + 3 ≤12

2w ≤ 9

w ≤ 4.5

w² + 3w - 28 ≥ 0

(w + 7)(w - 4) ≥ 0

w + 7 ≥ 0

w ≥ -7

Well, duh, the measurement can't be negative at all, so it has to be greater than 0, but even 1(4) is not at least 28, so this answer is out.

w - 4 ≥ 0

w ≥ 4

So, our width is at least 4m but not more than 4.5, because anything more than 4.5 would make our perimeter more than 24m.