A rectangle has a length that is 2 less than 3 times the width. If the perimeter is 84, find the dimensions of the rectangle.
P = 2L + 2W
84 = 2(3W - 2) + 2W
84 = 8W - 4
88 = 8W
? = W
To find the dimensions of the rectangle, we need to set up an equation based on the given information and solve for the width and length.
Let's assume the width of the rectangle is "w".
According to the problem, the length of the rectangle is 2 less than 3 times the width. So, the length can be represented as (3w - 2).
The perimeter of a rectangle is calculated by adding the lengths of all four sides, which in this case would be 2 times the width added to 2 times the length. Therefore, the equation for the perimeter can be written as:
Perimeter = 2w + 2(3w - 2)
Since it is given that the perimeter is 84, we can set up the equation:
84 = 2w + 2(3w - 2)
Now, let's solve this equation to find the value of "w" (the width):
84 = 2w + 6w - 4
84 = 8w - 4
84 + 4 = 8w
88 = 8w
w = 88/8
w = 11
So, the width of the rectangle is 11.
Now, substitute this value back into the equation for the length to find the value of the length:
Length = 3w - 2
Length = 3(11) - 2
Length = 33 - 2
Length = 31
Therefore, the dimensions of the rectangle are width = 11 and length = 31.