Question

The longest rod that fits into a box is 25 cm. If the length and the breadth of the box are 16 cm and 12 cm, find the height of the box.

Answer 1

Given:

• Length of the box L = 16 cm
• Breadth of the box B = 12 cm 
• Diagonal of the box (the longest rod) D = 25 cm
• Height of the box H = ?

Step 1: Formula for the diagonal of a cuboid

The formula for the diagonal D of a cuboid is:

`D = sqrt(L^2 + B^2 + H^2)`

Step 2: Substitute the known values

Substitute L = 16 cm, B = 12 cm and D = 25 cm into the equation:

`25 = sqrt(16^2 + 12^2 + H^2)`

`25 = sqrt(256 + 144 + H^2)`

`25 = sqrt(400 + H^2)`

Step 3: Solve for H²

Square both sides of the equation to eliminate the square root:

25² = 400 + H²

625 = 400 + H²

H² = 625 – 400 = 225

Step 4: Find H

Take the square root of both sides:

H = `sqrt(225)` = 15 cm