Question

consider these rectangles.
select all the expressions that represent the difference of the length - to - width ratios for rectangle a and rectangle b, where w is the width of rectangle a.
\\( \frac { w + 5 } { w } - \frac { w + 1 } { 2 w } \\)
\\( \frac { 4 } { 3 w } \\)
\\( \frac { w + 5 } { w + 1 } - \frac { w } { 2 w } \\)
\\( \frac { w + 9 } { 2 w } \\)
\\( \frac { w + 11 } { 2 w } \\)

Explanation:

Step1: Calculate the length - to - width ratio for rectangle A

The length of rectangle A is \(w + 5\) and the width is \(w\). So the ratio is \(\frac{w + 5}{w}\).

Step2: Calculate the length - to - width ratio for rectangle B

The length of rectangle B is \(w + 1\) and the width is \(2w\). So the ratio is \(\frac{w + 1}{2w}\).

Step3: Find the difference of the ratios

The difference is \(\frac{w + 5}{w}-\frac{w + 1}{2w}\).
Now, find a common denominator (\(2w\)):

$$
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$$

Answer:

A. \(\frac{w + 5}{w}-\frac{w + 1}{2w}\), D. \(\frac{w + 9}{2w}\)