Applications of the Pythagorean Theorem

Examples, solutions, and videos to help Grade 8 students learn how to apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.

New York State Common Core Math Grade 8, Module 7, Lesson 18

Worksheets for Grade 8

Lesson 18 Student Outcomes
• Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.

Lesson 18 Summary
• We know some basic applications of the Pythagorean Theorem in terms of measures of a television, length of a ladder, area and perimeter of right triangles, etc.
• We know that there will be some three-dimensional applications of the theorem beyond what we have already seen.

Lesson 18 Classwork
Exercises 1–5

1. The area of the right triangle shown below is 36.46 in². What is the perimeter of the right triangle? Round your answer to the tenths place.
2. The diagram below is a representation of a soccer goal.
   a. Determine the length of the bar, c, that would be needed to provide structure to the goal. Round your answer to the tenths place.
   b. How much netting (in square feet) is needed to cover the entire goal?
3. The typical ratio of length to width that is used to produce televisions is 4:3.
   a. A TV with those exact measurements would be quite small, so generally the size of the television is enlarged by multiplying each number in the ratio by some factor of x. For example a reasonably sized television might have dimensions of 4 × 5:3 × 5, where the original ratio 4:3 was enlarged by a scale factor of 5. The size of a television is described in inches, such as a 60” TV, for example. That measurement actually refers to the diagonal length of the TV (distance from an upper corner to the opposite lower corner). What measurement would be applied to a television that was produced using the ratio of 4 × 5:3 × 5?
   b. A 42” TV was just given to your family. What are the length and width measurements of the TV?
   c. Check that the dimensions you got in part (b) are correct using the Pythagorean Theorem.
   d. The table that your TV currently rests on is 30” in length. Will the new TV fit on the table? Explain.
4. Determine the distance between the following pairs of points. Round your answer to the tenths place. Use graph paper if necessary.
   a. (7, 4) and (-3, -2)
   b. (-5, 2) and (3, 6)
   c. Challenge: (x₁, y₁) and (x₂, y₂). Explain your answer.
5. What length of ladder will be needed to reach a height of 7 feet along the wall when the base of the ladder is 4 feet from the wall? Round your answer to the tenths place.

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