To solve the problem of finding the dimensions of the rectangle where the length (L) is three times its width (W) and the perimeter is 72 inches, we can follow these steps:
1. Let W represent the width of the rectangle.
2. Since the length (L) is three times the width, we can express the length as [tex]\( L = 3W \)[/tex].
3. The formula for the perimeter (P) of a rectangle is given by [tex]\( P = 2L + 2W \)[/tex].
4. We know that the perimeter is 72 inches, so we set up the equation as [tex]\( 2L + 2W = 72 \)[/tex].
Now, substitute the expression for L into the perimeter equation:
[tex]\[ 2(3W) + 2W = 72 \][/tex]
Simplify the equation:
[tex]\[ 6W + 2W = 72 \][/tex]
Combine like terms:
[tex]\[ 8W = 72 \][/tex]
Solve for W by dividing both sides of the equation by 8:
[tex]\[ W = \frac{72}{8} \][/tex]
[tex]\[ W = 9 \][/tex]
Now that we have the width (W), we can find the length (L) using the relationship [tex]\( L = 3W \)[/tex]:
[tex]\[ L = 3 \times 9 \][/tex]
[tex]\[ L = 27 \][/tex]
Therefore, the dimensions of the rectangle are:
[tex]\[ 27x9 \][/tex]
