Find the length of the longest diagonal (in cm) of a cuboidal box of dimensions 1.2 cm × 1.3 cm × 1.5 cm (correct to two decimal places).

Correct — D. The longest diagonal of a cuboid is the space diagonal, √(l² + b² + h²), which runs from one corner to the opposite one through the middle of the box.

Square each dimension:
1.2² = 1.44
1.3² = 1.69
1.5² = 2.25

Sum = 5.38
√5.38 ≈ 2.3195, which to two decimal places is 2.32 cm → option (d).

Why the others are wrong

• (a)
  2.23 cm — 2.23 is 2.32 with its digits swapped and squares to 4.9729, well short of 5.38. It is a transcription slip rather than a different method.
• (b)
  2.35 cm — 2.35 squares to 5.5225, overshooting the required 5.38. The root sits at 2.3195, so the second decimal place is 2, not 5.
• (c)
  2.22 cm — 2.22 squares to 4.9284, nearly half a unit short of 5.38. That is the diagonal of a noticeably smaller box than the one given.

A cuboid carries two diagonals worth knowing apart.

The face diagonal lies on one face and uses two dimensions, √(l² + b²). The space diagonal cuts through the solid and uses all three, √(l² + b² + h²).

Longest diagonal always means the space diagonal, so every dimension enters.

Square and add first, then take the root once. Here 1.2², 1.3² and 1.5² are exact two-place decimals, so the sum 5.38 is exact and the only rounding is at the square root.

Key facts

• Space diagonal of a cuboid = √(l² + b² + h²).
• 1.2² + 1.3² + 1.5² = 1.44 + 1.69 + 2.25 = 5.38.
• √5.38 ≈ 2.3195, which is 2.32 to two decimal places.

Common traps

• Using √(l² + b²) and answering with a face diagonal
• Adding 1.2 + 1.3 + 1.5 instead of the squares
• Writing 2.23 for 2.32 — the printed options include the digit-swapped value

No directly related past PYQ was found.