Answer: length = 19 inches and width = 8 inches
Step-by-step explanation: To solve this problem, our first task is to set up variables.
Since the length of the rectangle is 5 inches less than 3 times its width, we can set up variables to represent this.
Variables
X ⇒ width
3x - 5 ⇒ length
To help set up our equation, I will draw a picture of the rectangle labeling the widths X and the lengths 3x - 5.
Going back to the original problem, the second sentence states that the perimeter of he rectangle is 54 inches. Remember that the perimeter is the distance around the rectangle.
Based on the picture I provided, our equation will read as followed.
X + X + (3x -5) + (3x - 5) = 54
8x - 10 = 54 ← simplify on the left side of the equation
+10 +10 ← add 10 on both sides
8x = 64
÷8 ÷8
X = 8
Therefore, the width of our rectangle is 8 inches and the length of our rectangle is (3 x 8) - 5 or 19.
