Final answer:
To find the dimensions of the rectangle with an area of 66 square yards and a length that is 7 yards less than three times its width, we set up and solve the equation w(3w - 7) = 66 for the width (w), then calculate the length using the expression 3w - 7.
Step-by-step explanation:
The student is asking to find the dimensions of a rectangle where the length is 7 yards less than three times the width, and the area is 66 square yards. To solve this, we can set up an equation based on the area of a rectangle, which is length times width. Let's denote the width as w and the length as 3w - 7. The equation for the area of the rectangle is:
w(3w - 7) = 66
Solving for w, we get:
3w^2 - 7w - 66 = 0
Factoring this quadratic equation, we find values of w. Since we're looking for positive dimensions, we'll take the positive value of w that satisfies the area. After finding the width, we can easily calculate the length by plugging the width into the length expression 3w - 7.
Thus, the dimensions of the rectangle would be the width w and the length 3w - 7 yards.