Chapter 12, Problem 10CR

To determine

To define: The dimension of a sheet of paper where area of paper is $143{\text{cm}}^2$ and the dimensions are consecutive odd integers.

The options are,

  $\begin{array}{c}\text{a}\text{.}l=9\text{cm}\\ \text{}w=\text{}\text{7}\text{cm}\\ \text{b}\text{.}l=11\text{cm}\\ \text{}w=\text{}9\text{cm}\\ \text{c}\text{.}l=15\text{cm}\\ \text{}w=\text{}13\text{cm}\\ \text{d}\text{.}l=11\text{cm}\\ \text{}w=\text{}13\text{cm}\end{array}$

Answer to Problem 10CR

The option $d$ is correct.

Explanation of Solution

Given information:

The area is given as:

  $143{\text{cm}}^2$ and dimensions are consecutive odd integers.

The provided options are,

  $\begin{array}{c}\text{a}\text{.}l=9\text{cm}\\ \text{}w=\text{}\text{7}\text{cm}\\ \text{b}\text{.}l=11\text{cm}\\ \text{}w=\text{}9\text{cm}\\ \text{c}\text{.}l=15\text{cm}\\ \text{}w=\text{}13\text{cm}\\ \text{d}\text{.}l=11\text{cm}\\ \text{}w=\text{}13\text{cm}\end{array}$

The area of rectangle is $l\times w$

Where, $l$ is length of rectangle and $w$ width of rectangle.

Since, the paper sheet is in rectangular shape so area of sheet is equal to area of rectangle.

Therefore, the multiply of length of the paper sheet and width of paper sheet equal to area of paper as,

  $l\times w=143$

Now check which option satisfy the condition $l\times w=143$

Option $\begin{array}{c}\text{a}\text{.}l=9\text{cm}\\ \text{}w=\text{}\text{7}\text{cm}\end{array}$

Put the values in equation $l\times w=143$ as,

  $\begin{array}{c}9\times 7=143\\ 63\ne 143\end{array}$

The multiply of $l\times w$ is not equal to provided area.

So, option $\text{a}$ is not correct.

Now,

  $\begin{array}{c}\text{b}\text{.}l=11\text{cm}\\ \text{}w=\text{}9\text{cm}\end{array}$

Put the values in equation $l\times w=143$ as,

  $\begin{array}{c}11\times 9=143\\ 99\ne 143\end{array}$

The multiply of $l\times w$ is not equal to provided area.

So, option $b$ is not correct.

Now,

  $\begin{array}{c}\text{c}\text{.}l=15\text{cm}\\ \text{}w=\text{}13\text{cm}\end{array}$

Put the values in equation $l\times w=143$ as,

  $\begin{array}{c}15\times 13=143\\ 195\ne 143\end{array}$

The multiply of $l\times w$ is not equal to provided area.

So, option $c$ is not correct.

Now,

Check for the option $\begin{array}{c}\text{d}\text{.}l=11\text{cm}\\ \text{}w=\text{}13\text{cm}\end{array}$

Put the values in equation $l\times w=143$ as,

  $\begin{array}{c}11\times 13=143\\ 143=143\end{array}$

The multiply of $l\times w$ is equal to provided area and the dimensions also a consecutive odd integer.

So, option $d$ is not correct.