The dimensions of the rectangle are found by setting up the equation for the area, 66 = (3w - 7) × w, and solving the quadratic equation 3w^2 - 7w - 66 = 0 to find the width (w) and the length (3w - 7). The dimensions are 6 ft in width and 11 ft in length.
To find the dimensions of the rectangle with an area of 66 ft2 where the length is 7 ft less than three times the width, we can use the formula for the area of a rectangle: Area = length × width. Let's denote the width as 'w' and the length as '3w - 7' (because it is 7 ft less than three times the width). Now, we can set up the equation:
66 = (3w - 7) × w
Expanding the equation, we get:
66 = 3w2 - 7w
This is a quadratic equation which can be rewritten as:
3w2 - 7w - 66 = 0
Using the quadratic formula or factoring, we solve for 'w'. Once we find the value of 'w', we can get the length by calculating '3w - 7'. After solving, we find that 'w' and the length are:
Width 'w' = 6 ft
Length '3w - 7' = 11 ft
Therefore, the dimensions of the rectangle are 6 ft in width and 11 ft in length.