Question

The internal dimensions of a rectangular box are 12 cm x  `x` cm x 9 cm. If the length of the longest rod that can be placed in this box is 17 cm; find `x`.   

Answer 1

Length of longest rod = Length of the diagonal of the box

17 = `sqrt(12^2 + x^2 + 9^2)`
17² = 12² + x² + 9²
x² = 17² - 12² -9² 
x² = 289 - 144 - 81
x² = 64
x = 8 cm