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. Wha
t are the smallest possible dimensions for the rectangle?
2 answers:
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
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
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