Chapter 7.3, Problem 34WE

To determine

To Find : The value of x.

Answer to Problem 34WE

The value of x is 20.

Explanation of Solution

Given information:

Consider a card, have a length 40 and width of x. It is cut off in four congruent pieces with each piece similar to each other.

The first and last terms of a proportion, $a:b=c:d$ are called extremes and the middle terms are the means.

Means-extremes Property of proportions: The product of the extremes equals to the product of means.

  $\frac{a}{b}=\frac{c}{d}$ is equivalent to $ad=bc$ .

Now consider a card, as shown in the textbook, have a length 40 and width of x. It was cut off in four congruent pieces with each piece similar to each other.

  $\frac{I_R}{l_r}=\frac{w_k}{w_r}$ is equivalent to $l_R{w}_r=l_r{w}_R$

Where

  $l_R$ is length of original card.

  $w_R$ is width of original card.

  $l_r$ is length of one piece.

  $w,$ is the width of one piece.

Therefore,

  $\begin{array}{l}\frac{I_R}{I_r}=\frac{w_R}{w_r}\\ \frac{40}{x}=\frac{x}{10}\\ x^2=400\\ x=\pm 20\end{array}$

Width cannot be negative.

Hence, the value of x is 20.