Since we know the area and the length of the rectangular cloth, we can use the formula for the area of a rectangle to find the width.
The formula is:
Area = (length)(width)
A = l * w

Replace the area and the length with the values given.

\(\displaystyle{6}{x}^{{2}}-{19}{x}-{85}={\left({2}{x}+{5}\right)}\cdot{w}\)

Our goal is to get w by itself since we want to find the width. We can divide the length on both sides to get the width by itself.

\(\displaystyle\frac{{{6}{x}^{{2}}-{19}{x}-{85}}}{{{2}{x}+{5}}}={w}\)

The numerator of the fraction is a quadratic equation. We can simplify the equation to see if we can simplify the fraction any further.

\(\displaystyle\frac{{{\left({2}{x}+{5}\right)}{\left({3}{x}-{17}\right)}}}{{{2}{x}+{5}}}={w}\)

We can simplify the fraction even further.

\(\displaystyle\frac{{{1}{\left({3}{x}-{17}\right)}}}{{1}}={w}\)

w = 3x -17

The width of the rectangular cloth is (3x - 17) cm.

Replace the area and the length with the values given.

\(\displaystyle{6}{x}^{{2}}-{19}{x}-{85}={\left({2}{x}+{5}\right)}\cdot{w}\)

Our goal is to get w by itself since we want to find the width. We can divide the length on both sides to get the width by itself.

\(\displaystyle\frac{{{6}{x}^{{2}}-{19}{x}-{85}}}{{{2}{x}+{5}}}={w}\)

The numerator of the fraction is a quadratic equation. We can simplify the equation to see if we can simplify the fraction any further.

\(\displaystyle\frac{{{\left({2}{x}+{5}\right)}{\left({3}{x}-{17}\right)}}}{{{2}{x}+{5}}}={w}\)

We can simplify the fraction even further.

\(\displaystyle\frac{{{1}{\left({3}{x}-{17}\right)}}}{{1}}={w}\)

w = 3x -17

The width of the rectangular cloth is (3x - 17) cm.