Question

Find the length of the longest pole that can be placed in a room 12 m long, 8m broad and 9 m high

• A. 15m
• B. 17m
• C. 13m
• D. 16m

Answer 1

Answer:

B. 17m

Understanding the Problem: Longest Pole in a Rectangular Room

Key Concept: Diagonal of a Cuboid

• The problem asks for the length of the longest pole that can fit inside a rectangular room (a cuboid). This is equivalent to finding the space diagonal of the cuboid.

• A cuboid has three dimensions: length (l), breadth (b), and height (h).

Formula for Space Diagonal

• The length of the space diagonal (d) of a cuboid is given by the formula: $d = \sqrt{(l^2 + b^2 + h^2)}$.

• This formula is derived from applying the Pythagorean theorem twice. First, find the diagonal of the base (d_base = sqrt(l^2 + b^2)), and then use this base diagonal and the height to find the space diagonal ( $\sqrt(d_{base}^2 + h^2)$).

Applying the Formula to the Given Dimensions

• Given dimensions:

  • Length (l) = 12 m

  • Breadth (b) = 8 m

  • Height (h) = 9 m

• Substitute these values into the formula:

• $d =\sqrt{(12^2 + 8^2 + 9^2)}$

• Calculate the squares:

  • 12^2 = 144

  • 8^2 = 64

  • 9^2 = 81

• Sum the squares:

• 144 + 64 + 81 = 289

• Find the square root of the sum:

• $d = \sqrt{(289)}$

• d = 17 m