Question

The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is the greatest possible value for the width? Write an inequality to model the problem.
A. 2w + 2 • (3w) ≥112
B. 2w + 2 • (3w) < 112
C. 2w + 2 • (3w) > 112
D. 2w + 2 • (3w) ≤112


Question 2.2. The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible value for the width?
A. 40 cm
B. 19.2 cm
C. 16 cm
D. 8 cm

Answer 1

Q2. The answer is D. 2w + 2 • (3w) ≤112

The perimeter of a rectangle is: P = 2w + 2l         (w - weight, l - length)

The perimeter is at most 112 centimeters: P ≤ 112
The length of a rectangle is three times its width: l = 3w

P ≤ 112
2w + 2l ≤ 112

l = 3w
2w + 2 * (3w) ≤ 112



Q2.2. The answer is D. 8 cm

The perimeter of a rectangle is: P = 2w + 2l         (w - weight, l - length)

The length of a rectangle is five times its width: l = 5w
The perimeter is at most 96 centimeters: P ≤ 96

P ≤ 96
2w + 2l ≤ 96

l = 5w
2w + 2 * 5w ≤ 96
2w + 10w ≤ 96
12w ≤ 96
w ≤ 96 : 12
w ≤ 8 cm

Answer 2

I hope this helps you