Final answer:
To find the dimensions of the rectangle, we define the width as w and the length as 3w. Using the perimeter formula 2l + 2w = 40, we solve for w and find it to be 5 inches and hence, the length is 15 inches.
Step-by-step explanation:
The question asks us to find the length and width of a rectangle where the length is three times the width and the perimeter is 40 inches. To solve this, we can set up a system of equations based on the given information.
Step 1: Understand and Define Variables
Let's define our variables. Let w be the width of the rectangle. Therefore, the length l will be 3 times the width, so l = 3w.
Step 2: Set Up Equations
The perimeter P of a rectangle is given by the formula P = 2l + 2w. Since we know the perimeter is 40 inches, we can write the equation 2(3w) + 2w = 40.
Step 3: Solve the Equation
Simplifying the equation, we get 6w + 2w = 40, which simplifies further to 8w = 40. Dividing both sides by 8 gives us w = 5. Knowing the width, we can find the length by multiplying it by 3 to get l = 15.
Answer
The width of the rectangle is 5 inches and the length is 15 inches.