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.

Answer 1

Answer: The answer is NO. Explained below.

Step-by-step explanation:  Given that Zahra has a number of rectangles of different sizes which are made of paper. Also, the length of every rectangle is 5 cm more than its breadth.

We are to find whether the relationship between lengths and breadths of rectangles is proportional or not.

Let,  'l' represents the length and 'b' represents the breadth of any of these rectangles, then according to the given information, we can write

l = b + 5.

For a proportional relationship, we need a relation of the form

l = k × b, which is not always possible in the given case.

For example, if l = 8, b = 3, and l=9, b=4 then we cannot write

l = k × b, for a constant k.

Hence there is no proportional relationship  between the lengths and widths of these rectangles.

Thus, the answer is NO. Hence explained.

Answer 2

Answer:

Yes, there is a proportional relationship between the lengths and widths of the rectangles.

Step-by-step explanation:

A rectangle is a quadrilateral with opposite sides to be equal. Its area can be determined by: A = length × width.

And its perimeter can be determined by: P = 2 (length + width).

Considering the given question, the paper rectangles of different sizes have a common property; each is 5 centimeters longer than its width. Therefore, the length for each is determined by the value of the width.

Thus,

     length = width + 5

⇒            l = w + 5

This expression shows the relationship between the length and widths of the rectangles.