The length of a rectangle is 9 feet longer than twice the width. If the perimeter is 90 feet, find the length and width of the rectangle?
P = 2L + 2W
90 = 2(2W + 9) + 2W
90 = 6W + 18
90 - 18 = 6W
72 = 6W
12 = W
24 + 9 = L
Let's solve this step-by-step.
Step 1: Let's assign variables for the length and width.
Let's assume the width of the rectangle is "W" feet.
Step 2: According to the statement, the length is 9 feet longer than twice the width.
So, the length is (2W + 9) feet.
Step 3: The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
Step 4: Substituting the values into the formula, we have:
90 = 2 * ((2W + 9) + W)
Step 5: Simplifying the equation, we have:
90 = 2 * (3W + 9)
45 = 3W + 9
3W = 45 - 9
3W = 36
W = 36/3
W = 12
Step 6: Now that we have the width, we can find the length.
Length = 2W + 9 = 2(12) + 9 = 24 + 9 = 33
Step 7: The length of the rectangle is 33 feet, and the width is 12 feet.
To find the length and width of the rectangle, we need to set up a system of equations using the information given.
Let's denote the width of the rectangle as "w" feet.
According to the problem, the length is 9 feet longer than twice the width, which can be expressed as 2w + 9 feet.
The perimeter of a rectangle is the sum of all its sides, which in this case is:
2(length + width) = 90 feet
2(2w + 9 + w) = 90
Now we can solve the equation for w to find the width:
2(3w + 9) = 90
6w + 18 = 90
6w = 72
w = 12
So, the width of the rectangle is 12 feet.
To find the length, we substitute the width value back into the expression for the length:
Length = 2w + 9
Length = 2(12) + 9
Length = 33
Therefore, the length of the rectangle is 33 feet and the width is 12 feet.