w - width
3w - 1 - length
54 in - perimeter
w + w + (3w - 1) + (3w - 1) = 8w - 2 - perimeter
The equation:
8w - 2 = 54 add 2 to both sides
8w = 56 divide both sides by 8
w = 7
3w - 1 = 3(7) - 1 = 21 - 1 = 20
The perimeter of the rectangle is twice the sum of the length and the width.The length of the rectangle is 20 inches long.
Given information-
The length of a rectangle is one inch less than three times its width.
The perimeter of the rectangle is 54 inches.
The perimeter of the rectangle is the boundary by which the rectangle is covered. The perimeter of the rectangle is twice the sum of the length and the width.
It can be given as,
[tex]P=2(a+b)[/tex]
Here,[tex]a[/tex] is the length of the rectangle and [tex]b[/tex] is the width of the rectangle.
Now it is given that the length of a rectangle is one inch less than three times its width. Suppose the length of the rectangle is [tex]x[/tex] inches long. Thus the width [tex]y[/tex] of the rectangle is,
[tex]=\dfrac{x+1}{3} =\dfrac{x}{3} +\dfrac{1}{3}[/tex]
Thus the perimeter of the rectangle is,
[tex]\begin{aligned}\\P&=2(x+\dfrac{x}{3}+\dfrac{1}{3} )\\54-\dfrac{2}{3} &=2\times\dfrac{3x+x}{3} \\\dfrac{160}{3} &=\dfrac{8x}{3}\\160&=8x\\x&=20\\\end[/tex]
Hence the length of the rectangle is 20 inches long.
Learn more about the perimeter of rectangle here;
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