Exercise 12 Page 457

We are going to use that the park and the model of the park are similar in order to find the width of the park. When we know the park's width and height we can then calculate its perimeter and area.

Width of the Park

We are told that the park is $800$ yards long. Here, we want to know its length in feet. Recall that one yard equals three feet. Let's make a diagram illustrating the situation. Since we are making a scale model of the park, we know that the rectangles are similar. In similar polygons corresponding sides are proportional. Let's use this for the park and the model of the park.

Perimeter of the Park

The perimeter of a rectangle is the sum of two times its length and two times its height. We know that the park's length is $2400$ feet and that its width is $1680$ feet. Let's use this to find its perimeter. The park's perimeter is $8160$ feet, which is equivalent to $\frac{8160}{3}=2720$ yards.

Area of the Park

To find the park's area we will use the formula for the area of a rectangle. Let's substitute the park's length and width into the formula to find its area. We have found that the park's area is $4032000{\text{ ft}}^2.$ Recall that nine square feet equals one square yard.