Find the length of the diagonal of a cuboid with dimensions 3, 4, and 12 units.

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Question: Find the length of the diagonal of a cuboid with dimensions 3, 4, and 12 units. (2020)

Options:

Correct Answer: √153

Exam Year: 2020

Solution:

Diagonal = √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13.

Find the length of the diagonal of a cuboid with dimensions 3, 4, and 12 units. (2020)

Find the length of the diagonal of a cuboid with dimensions 3, 4, and 12 units. (2020)

Step 1: Identify the dimensions of the cuboid. The dimensions are 3 units, 4 units, and 12 units.
Step 2: Write down the formula for the diagonal of a cuboid, which is Diagonal = √(length² + width² + height²).
Step 3: Substitute the dimensions into the formula: Diagonal = √(3² + 4² + 12²).
Step 4: Calculate each squared value: 3² = 9, 4² = 16, and 12² = 144.
Step 5: Add the squared values together: 9 + 16 + 144 = 169.
Step 6: Take the square root of the sum: √169 = 13.
Step 7: Conclude that the length of the diagonal of the cuboid is 13 units.

Pythagorean Theorem in 3D – The question tests the application of the Pythagorean theorem to find the diagonal of a three-dimensional shape, specifically a cuboid.