Chapter 6.6, Problem 50E

To determine

To calculate: If the tarp is similar to the infield.

Answer to Problem 50E

The tarp and the infield are similar.

Explanation of Solution

Given information:

Dimensions of the baseball infield = $90\text{ foot}$ by $90\text{ foot}$ .

The tarp extends $\text{15 feet}$ beyond each edge of the infield.

Calculation:

To find if the tarp is similar to the infield, find the ratio of the side lengths of the corresponding sides of the tarp and infield. If the ratios are equal, the tarp and the infield are similar. Since the tarp extends $\text{15 feet}$ beyond each edge of the infield, the length of each side the tarp will be $90+15+15=120\text{ feet}$ .

Ratio of the corresponding side length=

  $\begin{array}{l}\frac{\text{Length of tarp}}{\text{Length of infield}}\underset{\_}{?}\frac{\text{Width of tarp}}{\text{Width of infield}}\text{ [Write proportion]}\\ \frac{120}{90}=\frac{120}{90}\text{ [Substitute values]}\\ \frac{4}{3}=\frac{4}{3}\text{ [Divide out common factors]}\end{array}$

Since the ratio of the corresponding sides are equal, the tarp and the infield are similar.