Answer:
[tex]\displaystyle w = \sqrt{10}\text{ yd}[/tex]
Step-by-step explanation:
We are given the area and length of a rectangle and we want to determine the width.
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = \ell w[/tex]
Substitute in known values:
[tex]\displaystyle (3\sqrt{50}) = (3\sqrt{5})w[/tex]
Solve for the width w:
[tex]\displaystyle \begin{aligned} w & = \frac{3\sqrt{50}}{3\sqrt{5}} \\ \\ & = \frac{\sqrt{10 \cdot 5}}{\sqrt{5}} \\ \\ & = \frac{\sqrt{10}\cdot \sqrt{5}}{\sqrt{5}} \\ \\ &= \sqrt{10} \text{ yd}\end{aligned}[/tex]
In conclusion, the width of the rectangle is √10 yards.
