Share

## The length of a rectangle is 5 times larger than x. The width is 4 cm less than the length. The perimeter is at least 96 cm. What are the sm

Question

The length of a rectangle is 5 times larger than x. The width is 4 cm less than the length. The perimeter is at least 96 cm. What are the smallest possible dimensions for the rectangle?

in progress
0

Mathematics
3 years
2021-08-21T10:46:36+00:00
2021-08-21T10:46:36+00:00 2 Answers
6 views
0
## Answers ( )

Answer:width = 10 cm

length = 14 cm

The smallest dimension is 10 cm.

Step-by-step explanation:2x + 2(x + 4) ≥ 48

Solve for x.

2x + 2x + 8 ≥ 48

4x + 8 ≥ 48

4x ≥ 40

x ≥ 10

We know that the perimeter of a rectangle = 2(l + w)l = lengthw = widthIn our problem,l = 5xw = 5x – 4Let’s create an inequality to help us solve this problem.2(5x + (5x – 4)) ≥ 96Let’s start off by simplifying the terms inside the parentheses.2(10x – 4) ≥ 96Distribute the 220x – 8 ≥ 96Add 8 to both sides.20x ≥ 104Divide both sides by 20x ≥ 5.2Let’s plug 5.2 into x for our length and width.Length = 5x = 5(5.2) = 26 cmWidth = 5x – 4 = 5(5.2) – 4 = 26 – 4 = 22 cmThe smallest possible dimensions for the rectangle are, length = 26 cm and width = 22 cm