Chapter 6.5, Problem 42HP

To determine

To find: the product of the length and width. To find the length proportional to the width.

Answer to Problem 42HP

The length varies inversely with the width.

The length is not proportional to width as it varies inversely with the width.

Explanation of Solution

Given information:

Rectangle ABCD has afixed area. As the length $\mathcal{l}$ and the width $w$ change.

Calculation:

A rectangle $ABCD$ has fixed area.

The length $l$ and the width $w$ of the rectangle changes.

The area of rectangle is equal to product of its length and breadth.

  $Area=l\times w$ .

Since the area of rectangle is fixed.

Therefore, the product of length and width of the rectangle is also fixed, that is, constant.

Hence, the product of length and width of the rectangle is fixed.

This implies as follows:

  $\begin{array}{c}l\times w=\text{constant}\\ \text{l=}\frac{\text{constant}}{w}\end{array}$

Thus, the length varies inversely with the width.

Hence, the length is not proportional to width as it varies inversely with the width.