Answer :
Answer:
Length of the rectangle = 14.5 inches
Width of the rectangle = 37.5 inches
Step-by-step explanation:
Let the length of a rectangle = a inches
Since, width of the rectangle is 6 inches less than 3 times the length,
w = 3a - 6
Perimeter of the rectangle = 104 inches
Formula to calculate the perimeter of a rectangle = 2(length + width)
104 = 2[a + (3a - 6)]
2a + 2(3a - 6) = 104 → [Starting equation]
8a - 12 = 104 → [Distributive property]
8a - 12 + 12 = 104 + 12 → [Addition property of equality]
a = [tex]\frac{116}{8}=14.5[/tex] → [Division property of equality]
a). width of the rectangle = (3a - 6) = 37.5 inches
b). length of the rectangle = 14.5 inches
The width of the rectangle is 37.5 inches and the length of the rectangle is 14.5 inches.
The perimeter of a rectangle is represented as follows:
perimeter = 2l + 2w
where
w = width
l = length
Therefore,
perimeter = 104 inches
let
the length = a
Therefore,
width = 3a - 6
Therefore,
104 = 2a + 2(3a - 6)
104 = 2a + 6a - 12
116 = 8a
a = 116 / 8
a = 14.5 inches
width = 3(14.5 ) - 6 = 37.5 inches
Therefore, the width of the rectangle is 37.5 inches and the length of the rectangle is 14.5 inches.
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