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.

Given Information

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


Define the length and width

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


Formula

Perimeter = 2(Length + Width)


Apply formula and solve for x

2 (2x - 4 + x) < 78


Combine like terms in the bracket

2 (x - 4) < 78


Remove the bracket

2x - 8 < 78


Add 8 on both sides

2x < 78 + 8
2x < 86


Divide by 2 through

2x < 86
x < 89 ÷ 2
x < 45.5


Identify the bigger integer that is smaller than 45.5

max integer for x = 45


Width = 45cm

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