Final answer:
To find the width of the rectangle, we can use the formula for the area of a rectangle, which is length multiplied by width. The length of the rectangle is given as 9 yards more than twice the width. After solving the quadratic equation, we find that the width of the rectangle is 15 yards.
Step-by-step explanation:
To find the width of the rectangle, we can use the formula for the area of a rectangle, which is length multiplied by width. Let's call the width x. The length of the rectangle is given as 9 yards more than twice the width. So the length can be expressed as 2x + 9.
The area of the rectangle is given as 731 square yards. So we have the equation (2x + 9) * x = 731. Simplifying this equation, we get 2x^2 + 9x - 731 = 0.
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. When we solve for x, we find that x is approximately equal to 15 yards. Therefore, the width of the rectangle is 15 yards.