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 units. (2022)

Options:

Correct Answer: √49

Exam Year: 2022

Solution:

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

Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6 units. (2022)

Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6 units. (2022)

Step 1: Identify the dimensions of the rectangular box. They are 2 units, 3 units, and 6 units.
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: State the final answer: The length of the diagonal is 7 units.

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