Exploring Applications of the Pythagorean Theorem

This video tutorial covers various math problems for 8th-grade students, focusing on the Pythagorean Theorem, geometry, and scientific notation. It includes practical applications such as calculating the length of a brace for a door, determining if a tray can fit through a trash can opening, and identifying valid side lengths for right triangles. The tutorial also explores comparing large numbers using scientific notation, finding points on a line with a negative slope, and analyzing a jump rope contest to determine who jumps more in a given time.

What formula is used to calculate the length of the brace?

• a*b = c^2

• a^2 + b^2 = c^2

• 2a + 2b = c

• a^2 - b^2 = c^2

What is the approximate length of the brace needed?

• 3.5 feet

• 4 feet

• 5 feet

• 4.47 feet

Why does Jada believe the tray cannot fall through the trash can opening?

• The tray is too heavy.

• The shortest side of the tray is longer than the opening's edges.

• The tray is made of sturdy material.

• The trash can opening is covered.

What is the diagonal length of the trash can's opening?

• Approximately 11.4 inches

• 10 inches

• 9 inches

• 12 inches

Which set of numbers represents the sides of a right triangle?

• 8, 7, 15

• 8, 11, 129

• 1, 2, 3

• 4, 10, 84

Which of these is not a set of side lengths for a right triangle?

• All of the above

• 1, 2, 3

• 4, 10, 84

• 8, 7, 15

Which number is 3 times larger?

• 20 x 10^4 compared to 6 x 10^5

• None of the above

• 1.5 x 10^12 compared to 3 x 10^12

• 12 x 10^9 compared to 4 x 10^9

How many times larger is 3 x 10^12 compared to 1.5 x 10^12?

• 2 times

• 4 times

• 1.5 times

• 3 times

Which point could be on the same line with a negative slope as point (3,5)?

• (2, 0)

• (6, 5)

• (4, 7)

• (5, 4)

Who jumps more times in two minutes?

• Information not provided

• Noah

• They jump the same number of times

• Han