Pythagorean Theorem Applications and Problems

The video tutorial covers the Pythagorean theorem, explaining its application to right triangles and extending its use to 3D objects like rectangular prisms. It includes examples and guided practice to help students understand and apply the theorem in various scenarios.

What is the Pythagorean Theorem used for?

• Determining the volume of a cube

• Measuring the circumference of a square

• Finding the sides of a right triangle

• Calculating the area of a circle

In a right triangle, if one leg is 3 inches and the other is 4 inches, what is the length of the hypotenuse?

• 6 inches

• 5 inches

• 7 inches

• 8 inches

If the hypotenuse of a right triangle is 10 and one leg is 5, what is the length of the other leg?

• 5√3

• 5

• √75

• 10

How can the Pythagorean Theorem be applied to find the diagonal of a rectangular prism?

• By using the formula a² + b² = c² on the base

• By calculating the volume first

• By measuring the surface area

• By using the formula a² + b² + c² = d²

What is the length of the diagonal of a box with dimensions 3x3x12 using the Pythagorean Theorem?

• √153

• 12.37

• All of the above

• 3√7

In the textbook exercise, what is the area of the unshaded square if the hypotenuse is labeled as C?

• C²

• A x B

• B²

• A² + B²

What is the greatest length in whole inches that a part could be if it fits in a box measuring 4x4x14 inches?

• 14 inches

• 13 inches

• 15 inches

• 16 inches

If a triangle has sides of 24 and 10, what is the length of the hypotenuse?

• 32

• 30

• 28

• 26

How can you use the Pythagorean Theorem to determine if a fishing rod will fit in a box?

• By comparing the rod's length to the box's length

• By checking the box's height

• By calculating the diagonal length

• By measuring the box's width

What is the formula for the Pythagorean Theorem?

• a² = b² + c²

• a + b = c²

• a² + b² = c²

• a² + b² = c