Step 1: Let's denote the width of the rectangle as x. Therefore, the length will be x + 6.
Step 2: The formula to calculate the perimeter of a rectangle is:
Perimeter = 2 * (length + width)
We know the perimeter is 40m, so we can set up our equation like this:
40 = 2 * ((x + 6) + x)
Step 3: Distribute the 2 into the parenthesis (multiply every term inside the parenthesis by 2):
40 = 2 * (x + 6) + 2 * x
This simplifies further to:
40 = 2x + 12 + 2x
Step 4: Combine like terms which results in:
40 = 4x + 12
Step 5: Then, we isolate x. First, subtract 12 from both sides of the equation:
40 - 12 = 4x + 12 - 12
Simplifying that gives us:
28 = 4x
Step 6: Finally, to solve for x, divide both sides of the equation by 4:
x = 28 / 4, which gives us x = 7.
So the width of the rectangle is 7 meters.
Step 7: To find the length of the rectangle, we recall that the length is x + 6, therefore the length is 7 + 6 = 13 meters.
Step 8: The area of a rectangle is calculated using the formula:
Area = length * width
Substituting the values for the length and width yields:
Area = 13 * 7
This gives us an area of 91 square meters.
Therefore, the width of the rectangle is 7 m, its length is 13 m, and its area is
Answer: 91 m^2.