Given:
The length of a rectangle is 3 inches less than three times its width.
The perimeter of the rectangle is 34 inches.
To find:
The dimensions of the rectangle.
Solution:
Let x be the width of the rectangle. Then, the length of a rectangle is 3 inches less than three times its width.
Length of the rectangle = 3x-3
Now, perimeter of the rectangle is
[tex]Perimeter=2(Length + Width)[/tex]
[tex]Perimeter=2(3x-3+x)[/tex]
The perimeter of the rectangle is 34 inches.
[tex]34=2(4x-3)[/tex]
[tex]34=8x-6[/tex]
[tex]34+6=8x[/tex]
[tex]40=8x[/tex]
Divide both sides by 8.
[tex]\dfrac{40}{8}=x[/tex]
[tex]5=x[/tex]
The value of x is 5. So, width of the rectangle is 5 inches.
[tex]Length=3x-3[/tex]
[tex]Length=3(5)-3[/tex]
[tex]Length=15-3[/tex]
[tex]Length=12[/tex]
Therefore, the length of the rectangle is 12 inches and the width of the rectangle is 5 inches.
