Final answer:
To solve for the dimensions of the rectangle, represent the width as w, forming the equation 50 = (3w - 5)w. The resulting quadratic equation is solved to obtain the width w, and subsequently the length using 3w - 5.
Step-by-step explanation:
The question asks us to find the dimensions of a rectangle given that the length is 5 yards less than three times the width and that the area of the rectangle is 50 square yards. Let w represent the width of the rectangle. Then the length l will be 3w - 5. To find the area (A) of a rectangle, we use the formula A = l × w. We know the area is 50 square yards, so we can set up the equation 50 = (3w - 5)w.
Solving for w, we get a quadratic equation: 3w^2 - 5w - 50 = 0. We can solve for w by factoring or using the quadratic formula. Once we find w, we can use it to calculate l as 3w - 5.
Finding the exact values will involve factoring the quadratic equation or using an alternative method like completing the square or utilizing the quadratic formula.