In this problem, we are told that the area of a rectangle is 28 square yards, and the length is 5 yards less than three times the width. We need to find the dimensions of the rectangle.

Let:

• $w$ represent the width of the rectangle.
• $l$ represent the length of the rectangle.

We are given the following information:

1. The length is 5 yards less than three times the width, so: $l = 3w - 5$
2. The area of the rectangle is 28 square yards, and the area is calculated as $\text{Area} = l \times w$. Thus: $l \times w = 28$

Substitute the expression for $l$ from the first equation into the second equation: $(3w - 5) \times w = 28$ Expand and simplify: $3w^2 - 5w = 28$ $3w^2 - 5w - 28 = 0$

This is a quadratic equation. We can solve it using the quadratic formula: $w = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(3)(-28)}}{2(3)}$ Simplify: $w = \frac{5 \pm \sqrt{25 + 336}}{6}$ $w = \frac{5 \pm \sqrt{361}}{6}$ $w = \frac{5 \pm 19}{6}$

So, $w$ can be: $w = \frac{5 + 19}{6} = \frac{24}{6} = 4$ or [ w = \frac{5 -