Chapter 5, Problem 7TP

Solution

To identify: The equation that relates $l$ and $w$.

The correct answer is option B.

Given information:

Consider a rectangle whose dimensions change but whose area remains constant. The rectangle's length $l$ varies inversely with its width $w$ . The diagram below shows the rectangle at one moment of time.

  

The options are:

  $w=0.67l$

  $lw=1.1524$

  $w=1.72l$

  $l=1.1524w$

Formula used:

Two variables $x\text{ and }y$ show inverse variation if they are related as below:

  $y=\frac{a}{x}$.

Where, $a$ is a constant.

Explanation:

It is given that the rectangle's length $l$ varies inversely with its width $w$ , so

  $\begin{array}{c}l=\frac{a}{w}\\ a=lw\mathrm{..........}\left(1\right)\end{array}$

Take the length and width from the given figure and substitute in equation (1).

  $\begin{array}{c}lw=1.72\times 0.67\\ =1.1524\end{array}$

Therefore, the correct answer is option B.