Question

zahra has paper rectangles of different sizes. every rectangle is 5 centimeters longer than it is wide. is there a proportional relationship between the lengths and widths of these rectangles? explain.

Explanation:

Step1: Let width be $w$ and length be $l$.

Given $l = w + 5$.

Step2: For proportional rectangles, the ratio of length to width should be constant.

Let's assume two rectangles with widths $w_1$ and $w_2$ and lengths $l_1=w_1 + 5$ and $l_2=w_2 + 5$. The ratio of lengths to widths for the first rectangle is $\frac{l_1}{w_1}=\frac{w_1 + 5}{w_1}=1+\frac{5}{w_1}$, and for the second rectangle is $\frac{l_2}{w_2}=\frac{w_2 + 5}{w_2}=1+\frac{5}{w_2}$.
If $w_1
eq w_2$, then $\frac{l_1}{w_1}
eq\frac{l_2}{w_2}$.

Answer:

There is no proportional relationship between the lengths and widths of these rectangles because the ratio of length to width is not constant for different - sized rectangles.