Diagonal Lengths in Rectangular Prisms

This lesson teaches how to find the length of a diagonal inside a rectangular prism using the Pythagorean Theorem. It begins with a review of the theorem and its application to right triangles. The lesson explains the differences between two-dimensional and three-dimensional figures and highlights the common misconception that solving for a diagonal in a rectangular prism is a one-step process. The lesson outlines the steps to solve for diagonal lengths, including writing equations, solving for unknowns, and verifying answers. It concludes with a practical example of calculating the diagonal using a table and verifying the solution.

What theorem is used to find the length of a diagonal inside a rectangular prism?

• Fundamental Theorem of Calculus

• Binomial Theorem

• Pythagorean Theorem

• Theorem of Relativity

What is a key difference between two-dimensional and three-dimensional figures?

• Three-dimensional figures have height, length, and width.

• Three-dimensional figures have only length and width.

• Two-dimensional figures have height, length, and width.

• Two-dimensional figures have height and width.

When solving for the diagonal in a rectangular prism, how many times might you need to apply the Pythagorean Theorem?

• Twice

• Once

• Four times

• Three times

In the example given, what is the length of side A after solving the base right triangle?

• 10 cm

• 20 cm

• 14.14 cm

• 24.5 cm

What is the length of the diagonal (side C) in the rectangular prism example?

• 24.5 cm

• 10 cm

• 20 cm

• 14.14 cm

What is the purpose of using a table in solving for the diagonal of a rectangular prism?

• To avoid using the Pythagorean Theorem

• To find the volume of the prism

• To organize side lengths and areas

• To make the problem more complex

What is the length of side B in the example provided?

• 24.5 cm

• 10 cm

• 20 cm

• 14.14 cm

What is the square root of the sum of the squares of sides A and B in the example?

• 14.14

• 20

• 24.5

• 600

What must be true for the solution of side A to be correct?

• 10 squared plus 10 squared equals 14.14 squared

• 10 squared plus 20 squared equals 14.14 squared

• 10 squared plus 10 squared equals 20 squared

• 14.14 squared plus 20 squared equals 24.5 squared

What is the final step in verifying the solution for the diagonal of a rectangular prism?

• Checking the answers

• Drawing a diagram

• Writing equations

• Solving for unknowns