The length of a certain rectangle is 4 m greater than five times it's width. What are the dimensions of the rectangle if its perimeter is 20m??? please help i have no idea how to do this!
P = 2L + 2W
20 = 2(5W + 4) + 2W
20 = 10W + 8 + 2W
20 - 8 = 12W
12 = 12W
1 = W
thank you!
To solve this problem, let's break it down into steps:
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
To find the dimensions of the rectangle, we need to set up an equation using the given information.
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.