The length of the rectangle is 25 feet and the width of the rectangle is 9 feet.
It is given that,
- Length of a rectangle is 2 feet less than three times the width.
- Perimeter is 68 feet.
Explanation:
Let [tex]x[/tex] be the width of the rectangle. Then the length of the rectangle is [tex]3x-2[/tex].
Perimeter of a rectangle is:
[tex]P=2(\text{length}+\text{width})[/tex]
[tex]68=2(3x-2+x)[/tex]
[tex]68=2(4x-2)[/tex]
[tex]68=8x-4[/tex]
Isolate the variable.
[tex]68+4=8x[/tex]
[tex]\dfrac{72}{8}=x[/tex]
[tex]9=x[/tex]
Now, the length of the rectangle is:
[tex]3(9)-2=27-2[/tex]
[tex]3(9)-2=25[/tex]
Thus, the length of the rectangle is 25 feet and the width of the rectangle is 9 feet.
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