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?

Answer 1

width = 10 cm

length = 14 cm

The smallest dimension is 10 cm.

Explanation:

2x + 2(x + 4) ≥ 48

Solve for x.

2x + 2x + 8 ≥ 48

4x + 8 ≥ 48

4x ≥ 40

x ≥ 10

Answer 2

We know that the perimeter of a rectangle = 2(l + w)

l = length

w = width

In our problem,

l = 5x

w = 5x - 4

Let's create an inequality to help us solve this problem.

2(5x + (5x - 4)) ≥ 96

Let's start off by simplifying the terms inside the parentheses.

2(10x - 4) ≥ 96

Distribute the 2

20x - 8 ≥ 96

Add 8 to both sides.

20x ≥ 104

Divide both sides by 20

x ≥ 5.2

Let's plug 5.2 into x for our length and width.

Length = 5x = 5(5.2) = 26 cm

Width = 5x - 4 = 5(5.2) - 4 = 26 - 4 = 22 cm

The smallest possible dimensions for the rectangle are, length = 26 cm and width = 22 cm