Question

The length of a rectangle is 4 cm less than twice the width. express as an integer the maximum width of the rectangle when the perimeter is less than 78 cm.

Answer 1

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Given Information
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Length is 4cm less than twice the width
Perimeter is less than 79 cm

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Define the length and width
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Let the width be x
width = x
length = 2x - 4

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Formula
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Perimeter = 2(Length + Width)

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Apply formula and solve for x
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2 (2x - 4 + x) < 78

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Combine like terms in the bracket
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2 (x - 4) < 78

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Remove the bracket
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2x - 8 < 78

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Add 8 on both sides
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2x < 78 + 8
2x < 86

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Divide by 2 through
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2x < 86
x < 89 ÷ 2
x < 45.5

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Identify the bigger integer that is smaller than 45.5
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max integer for x = 45

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Answer: Width = 45cm
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