# Illustrative Mathematics Grade 8, Unit 8, Lesson 10: Applications of the Pythagorean Theorem

Learning Targets:

• I can use the Pythagorean Theorem to solve problems.

Related Pages
Illustrative Math

#### Lesson 10: Applications of the Pythagorean Theorem

Let’s explore some applications of the Pythagorean Theorem.

Illustrative Math Unit 8.8, Lesson 10 (printable worksheets)

#### Lesson 10 Summary

The following diagram explore some applications of the Pythagorean Theorem. #### Lesson 10.1 Closest Estimate: Square Roots

Which estimate is closest to the actual value of the expression? Explain your reasoning.

#### Lesson 10.2 Cutting Corners

Mai and Tyler were standing at one corner of a large rectangular field and decided to race to the opposite corner. Since Mai had a bike and Tyler did not, they thought it would be a fairer race if Mai rode along the sidewalk that surrounds the field while Tyler ran the shorter distance directly across the field. The field is 100 meters long and 80 meters wide. Tyler can run at around 5 meters per second, and Mai can ride her bike at around 7.5 meters per second.

1. Before making any calculations, who do you think will win? By how much? Explain your thinking.
2. Who wins? Show your reasoning.

#### Are you ready for more?

A calculator may be necessary to answer the following questions. Round answers to the nearest hundredth.

1. If you could give the loser of the race a head start, how much time would they need in order for both people to arrive at the same time?
2. If you could make the winner go slower, how slow would they need to go in order for both people to arrive at the same time?

#### Lesson 10.3 Internal Dimensions

Here are two rectangular prisms:

1. Which figure do you think has the longer diagonal? Note that the figures are not drawn to scale.
2. Calculate the lengths of both diagonals. Which one is actually longer?

#### Lesson 10 Practice Problems

1. A man is trying to zombie-proof his house. He wants to cut a length of wood that will brace a door against a wall. The wall is 4 feet away from the door, and he wants the brace to rest 2 feet up the door. About how long should he cut the brace?
2. At a restaurant, a trash can’s opening is rectangular and measures 7 inches by 9 inches. The restaurant serves food on trays that measure 12 inches by 16 inches. Jada says it is impossible for the tray to accidentally fall through the trash can opening because the shortest side of the tray is longer than either edge of the opening. Do you agree or disagree with Jada’s explanation? Explain your reasoning.
3. Select all the sets that are the three side lengths of right triangles.
4. For each pair of numbers, which of the two numbers is larger? How many times larger?
5. A line contains the point (3,5). If the line has negative slope, which of these points could also be on the line?
6. Noah and Han are preparing for a jump rope contest. Noah can jump 40 times in 0.5 minutes. Han can jump y times in x minutes, where y = 78x. If they both jump for 2 minutes, who jumps more times? How many more?

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 