Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6

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Question: Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6. (2023)

Options:

Correct Answer: √49

Solution:

Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.

Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6. (2023)

Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6. (2023)

Step 1: Identify the dimensions of the rectangular box. They are 2, 3, and 6.
Step 2: Write down the formula for the diagonal of a rectangular box: Diagonal = √(length² + width² + height²).
Step 3: Substitute the dimensions into the formula: Diagonal = √(2² + 3² + 6²).
Step 4: Calculate each square: 2² = 4, 3² = 9, and 6² = 36.
Step 5: Add the squared values together: 4 + 9 + 36 = 49.
Step 6: Take the square root of the sum: √49 = 7.
Step 7: Conclude that the length of the diagonal of the rectangular box is 7.

Pythagorean Theorem in 3D – The question tests the application of the Pythagorean theorem extended to three dimensions to find the diagonal of a rectangular box.