The length of a rectangle is 8 less than twice the length. If the perimeter of the rectangle is 194 inches, find the dimensions of the rectangle.
width=w
length=2w-8
2(w + 2w-8) = 194
To find the dimensions of the rectangle, let's assume that the length is represented by "L" and the width is represented by "W".
It's given that the length of the rectangle is 8 less than twice the width. So, from this information, we can write the equation:
L = 2W - 8
The perimeter of a rectangle is given by the formula:
Perimeter = 2(L + W)
Substituting the given value of perimeter (194 inches) and the equation for length into the formula, we get:
194 = 2((2W - 8) + W)
Simplifying the equation:
194 = 2(3W - 8)
194 = 6W - 16
Adding 16 to both sides of the equation:
210 = 6W
Dividing both sides by 6:
W = 35
Now that we have the value of W, we can substitute it back into the equation for the length:
L = 2W - 8
L = 2(35) - 8
L = 70 - 8
L = 62
So, the dimensions of the rectangle are length = 62 inches and width = 35 inches.