Algebra 1A - Applications

Question

The length of a rectangle is 6 inches more than the width. The perimeter of the rectangle can be no more than 48 inches. Write a compound inequality to represent the possible widths.

Answer 1

L = W + 6

P = 2L + 2W

P can't be more than 48

2(W + 6) + 2W ≤ 48

2W + 12 + 2W ≤ 48

4W ≤ 36

W ≤ 9 so 0 < W ≤ 9

Answer 2

P = 48

P/2 = 24 = L+W = W+6+W = 2W+6

2W =24-6 = 18

W = 18/2 = 9 inches = maximum Width

0 < W < 9 or in interval notation W is an element of the interval (0,9]

if W=9, L= 9+6 = 15

and P=9+15)2) = 48

if W = nearly zero, L= about 6 and P=about 12

12<P<48

6<L <15