Question

what is the length of the rod that can be put in a box of dimensions 35cm, 28cm and 21cm​

Answer 1

Given that,

Length of the box = 35 cm

Breadth of the box = 28 cm

Height of the box = 21 cm

To find,

The maximum length of the rod = ?

As we know,

The longest line segments in a rectangle are its diagonals. If we carefully observe the figure (in the attachment), it's cleared that the longest line segments are AC and BD.

So, the longest rod to be put inside a rectangular box can be fit in its diagonals.

As we know,

The length of the diagonal = $\sqrt{l^{2} + b^{2} + h^{2}}$

∴ the length of the diagonal = $\sqrt{35^{2} + 28^{2} + 21^{2}}$

∴ the length of the diagonal = $\sqrt{1,225 + 784 + 441}$

∴ the length of the diagonal = $\sqrt{2,450\:cm}$

∴ the length of the diagonal = 49.50 (approximately)

∴ The maximum length of the rod that can be put inside the box is 49.50 cm.