Chapter 6.4, Problem 2C

To determine

To state: whether a goal area is similar to the penalty area of the soccer field

Answer to Problem 2C

The ratios of the lengths of corresponding sides are not equal, so the goal area is not similar to the penalty area

Explanation of Solution

Given information:

From the figure provided in the question,

Length of the goal area is 19 yards

widthof the goal area is 6 yards

From figure 3,

length of the penalty area is 35 yards

width of the penalty area is 14 yards

Calculation:

In rectangle, the corresponding angles are congruent because all four angles are right angled. To decide if the rectangles are similar, determine whether the ratios of the lengths of corresponding sides are equal.

  $\begin{array}{l}\frac{\text{length of the penalty area}}{\text{length of goal area}}=\frac{\text{width of penalty area}}{\text{width of goal area}}\text{ write proportion}\\ \frac{35}{19}=\frac{14}{6}\text{ Substitute values}\\ \text{35 }·\text{ 6 = 19 }·\text{ 14 cross multiply}\\ \text{210}\ne \text{266 Multiply}\end{array}$

So, the ratio is unequal.

Therefore, the ratios of the lengths of corresponding sides are not equal, so the goal area is not similar to the penalty area