1. Lesson 7

1.2. Explore 2

Mathematics 20-2 M5 Lesson 7

Module 5: Radicals

 

There are times where you are given information about a situation, and you need to combine different formulas to develop an equation that will solve the problem.

 

The length of a soccer field is times the width. The diagonal of the field is 116.6 yd long.

 

What are the dimensions of the soccer field to the nearest yard?

 

Watch Soccer Field to see how the dimensions of the soccer field are determined.

 

 

This is a screenshot for Soccer Field.

 

This is a sketch of the problem presented. It shows a rectangle with the width of w, the length of five thirds w, and a diagonal measure of 116.6 yd.

Begin by stating any restrictions on variables. Then sketch a diagram and label it with any information that you have:

  • w ≥ 0
  • The diagonal is 116.6 yd.
  • The width is unknown: let the width = w.
  • The length is times the width: let the length = w.

The Pythagorean theorem can be used to set up an equation.

 

 

a2 + b2 = c2

 

 

 

Now the equation can be rearranged to isolate w.

 

 

 

The answer should be rounded to the nearest yard, so w = 60 yd.

 

Since the length of the soccer field can be calculated:

 

 

 

The width of the soccer field is 60 yd, and the length is 100 yd.