P = 2L + 2W
20 = 2(5W + 4) + 2W
20 = 10W + 8 + 2W
20 - 8 = 12W
12 = 12W
1 = W
20 = 2(5W + 4) + 2W
20 = 10W + 8 + 2W
20 - 8 = 12W
12 = 12W
1 = W
Step 1: Assign variables.
Let's assign variables to represent the width and length of the rectangle. We'll use "w" for the width and "l" for the length.
Step 2: Translate the given information into equations.
From the problem statement, we have two pieces of information. First, the length is 4 m greater than five times the width, which can be written as:
l = 5w + 4 (Equation 1)
Second, the perimeter of the rectangle is 20 m. The formula for the perimeter of a rectangle is:
perimeter = 2(length + width)
So, for this rectangle, it can be written as:
20 = 2(l + w) (Equation 2)
Step 3: Solve the system of equations.
Now, we'll use equations 1 and 2 to solve for the width and length of the rectangle.
First, substitute equation 1 into equation 2:
20 = 2((5w + 4) + w)
Step 4: Simplify and solve for w.
Distribute the 2 on the right side of the equation:
20 = 2(6w + 4)
Simplify further:
20 = 12w + 8
Subtract 8 from both sides of the equation:
12 = 12w
Divide both sides by 12:
w = 1
Step 5: Find the length.
Now that we have the value of w, we can substitute it back into equation 1 to find the length:
l = 5w + 4
l = 5(1) + 4
l = 5 + 4
l = 9
Step 6: Check the solution.
To check if the solution is correct, substitute the width and length values into the perimeter equation:
perimeter = 2(l + w)
20 = 2(9 + 1)
20 = 2(10)
20 = 20
The perimeter equation holds true, so our solution is correct.
Therefore, the dimensions of the rectangle are:
Width = 1 meter
Length = 9 meters
Let's assume the width of the rectangle is "w" meters.
According to the given information, the length of the rectangle is 4 meters greater than five times its width. So, the length would be (5w + 4) meters.
The formula for the perimeter of a rectangle is P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
Substituting the given values into the formula, we get:
20 = 2((5w + 4) + w)
Now, we can solve this equation to find the value of w (the width) and subsequently find the length.
1. Distribute the 2 to both terms inside the parenthesis:
20 = 2(5w + 4 + w)
2. Simplify the expression inside the parenthesis:
20 = 2(6w + 4)
3. Distribute the 2 to each term inside the parenthesis:
20 = 12w + 8
4. Move the constant term to the other side of the equation by subtracting 8 from both sides:
20 - 8 = 12w
12 = 12w
5. Divide both sides of the equation by 12 to solve for w:
w = 1
Now, we have found the width of the rectangle, which is 1 meter.
To find the length, substitute the value of w back into the expression for the length:
Length = 5w + 4
= 5(1) + 4
= 5 + 4
= 9
Therefore, the dimensions of the rectangle are 1 meter for the width and 9 meters for the length.