The length of a rectangle is 8 inches more than three times the width. The perimeter is 88 inches. Find the length and width
P = 2L + 2W
88 = 2(3W + 8) + 2W
88 = 6W + 16 + 2W
72 + 8W
9 = W
To solve this problem, we can start by defining our variables:
Let's assume the width of the rectangle is represented by the letter 'w'.
The length of the rectangle is 8 inches more than three times the width, which can be expressed as 3w + 8.
Now, we can set up an equation based on the given information. The perimeter of a rectangle is the sum of all its sides, so:
Perimeter = 2(length + width)
Since we're given that the perimeter is 88 inches, we can substitute the values into the equation and solve for the variables:
88 = 2((3w + 8) + w)
Let's simplify the equation:
88 = 2(4w + 8)
88 = 8w + 16
Subtract 16 from both sides:
72 = 8w
Now, divide both sides by 8:
w = 9
So, the width of the rectangle is 9 inches.
To find the length, substitute w = 9 back into the expression for the length (3w + 8):
Length = 3(9) + 8
Length = 27 + 8
Length = 35
Therefore, the length of the rectangle is 35 inches.
In conclusion, the width is 9 inches and the length is 35 inches.