The length of a rectangle is 3 feet less than 4 times the width. If the perimeter is 84 feet, find the dimension
width --- x ft
length = 4x - 3
2x) + 2(4x-3) = 84
solve for x, then sub into my definitions.
Let's solve this step-by-step.
Step 1: Assign variables. Let's say the width of the rectangle is "w" feet.
Step 2: According to the given information, the length is 3 feet less than 4 times the width. So the length can be represented as (4w - 3) feet.
Step 3: The perimeter of a rectangle is calculated by adding all four sides. In this case, the perimeter is given as 84 feet. The formula for the perimeter is: perimeter = 2(length + width).
Step 4: Plug in the given values into the formula. We have:
84 = 2((4w - 3) + w)
Step 5: Distribute the 2 on the right side of the equation:
84 = 2(5w - 3)
Step 6: Simplify further:
84 = 10w - 6
Step 7: Add 6 to both sides of the equation to isolate the variable:
90 = 10w
Step 8: Divide both sides of the equation by 10 to solve for w:
w = 9
Step 9: Substitute the value of w back into the length equation:
length = 4w - 3 = 4(9) - 3 = 36 - 3 = 33
So, the dimensions of the rectangle are width = 9 feet and length = 33 feet.
To find the dimensions of the rectangle, we can set up two equations based on the given information.
Let's assume the width of the rectangle is "x" feet.
According to the problem, the length of the rectangle is 3 feet less than 4 times the width, which can be written as:
Length = 4x - 3
The perimeter of the rectangle is the sum of all four sides. In this case, it can be written as:
Perimeter = 2(Length + Width)
Since the perimeter is given as 84 feet, we can substitute the values into the equation:
84 = 2((4x - 3) + x)
Now, we can simplify and solve for x:
84 = 2(5x - 3)
84 = 10x - 6
10x = 90
x = 9
So, the width of the rectangle is 9 feet.
To find the length, we can substitute the value of x into the length equation:
Length = 4x - 3
Length = 4(9) - 3
Length = 36 - 3
Length = 33
Therefore, the dimensions of the rectangle are:
Width = 9 feet
Length = 33 feet