Question

The area of a rectangular cloth is (6x2 - 19x - 85) cm2.The length is (2x + 5) cm. Find the width.

Solid Geometry

The area of a rectangular cloth is $$(6x^2 - 19x - 85)$$ cm2. The length is (2x + 5) cm. Find the width.

2020-12-16
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.