Chapter 6.4, Problem 20E

a.

To determine

To explain: If the two computer screens are similar.

Answer to Problem 20E

Computer 1 and computer 2 are not similar.

Explanation of Solution

Given information:

The following table:

  

To find if the two computer screens are similar, determine whether the ratios of the lengths of corresponding sides are equal. Because all computer screens have four right angles, the corresponding angles are congruent.

  $\begin{array}{l}\frac{\text{Height of computer 1}}{\text{Height of computer 2}}\underset{\_}{?}\frac{\text{Width of computer 1}}{\text{Width of computer 2}}\text{ [Write proportion]}\\ \frac{9}{12}\underset{\_}{?}\frac{12}{15}\text{ [Substitute values]}\\ 9\cdot 15\underset{\_}{?}12\cdot 12\text{ [Form cross product]}\\ 135\ne 144\text{ [Multiply]}\end{array}$ .

The ratio of the lengths of corresponding sides are not equal so computer 1 and computer 2 are not similar.

b.

To determine

To explain: If the television screen is similar to either computer screen.

Answer to Problem 20E

The television is similar to computer 1 but not similar to computer 2.

Explanation of Solution

Given information:

The following table:

  

To find if the television is similar to computer 1, determine whether the ratios of the lengths of corresponding sides are equal.

  $\begin{array}{l}\frac{\text{Height of television}}{\text{Height of computer 1}}\underset{\_}{?}\frac{\text{Width of television}}{\text{Width of computer 1}}\text{ [Write proportion]}\\ \frac{18}{9}\underset{\_}{?}\frac{24}{12}\text{ [Substitute values]}\\ \text{ 18}\cdot 12\underset{\_}{?}24\cdot 9\text{ [Form cross product]}\\ 216=216\text{ [Multiply]}\end{array}$ .

The ratio of the lengths of corresponding sides are equal so television and computer 1 are similar.

To find if the television is similar to computer 2, determine whether the ratios of the lengths of corresponding sides are equal.

  $\begin{array}{l}\frac{\text{Height of television}}{\text{Height of computer 2}}\underset{\_}{?}\frac{\text{Width of television}}{\text{Width of computer 2}}\text{ [Write proportion]}\\ \frac{18}{12}\underset{\_}{?}\frac{24}{15}\text{ [Substitute values]}\\ \text{ 18}\cdot 15\underset{\_}{?}24\cdot 12\text{ [Form cross product]}\\ 270=288\text{ [Multiply]}\end{array}$ .

The ratio of the lengths of corresponding sides are not equal so television and computer 2 are not similar.

c.

To determine

To compare: The height and width ratios of the high definition TV and movie screen.

Answer to Problem 20E

The height and width ratios of the high definition TV and movie screen are equal.

Explanation of Solution

Given information:

The following table:

  

To compare the height to width ratios of the high definition TV and movie screen, first find the ratio of height to width of the high definition TV and the ratio of height to width of the movie screen.

Ratio of height to width of the high definition TV = $\frac{48}{27}$

Ratio of height to width of the movie screen = $\frac{32}{18}$

Comparing the two fractions:

  $\begin{array}{l}\frac{48}{27}\underset{\_}{?}\frac{32}{18}\text{ [Express in simplest form]}\\ \frac{16}{9}=\frac{16}{9}\end{array}$

Therefore, both the ratios are equal.