Question

write the formula of the diagonal of a cuboid

Answer 1

Answer:

$\sqrt{l^2 + b^2 + h^2}$

Step-by-step explanation:

Diagonal of a cuboid is given by :-

$\sqrt{l^2 + b^2 + h^2}$

Where, l is the length, b is the breadth and h is the height.

So, how does this formula comes?

Let's prove it out

Refer the attachment for figure

In figure, AD is the diagonal of the cuboid.

We know that, the angles would be right angles. So, by Pythagoras theorem,

AD² = AB² + BD²

Now, again, by Pythagoras theorem, we can see that

BD² = BC² + CD²

Now, substitue the value of BD² in first equation. We get

AD² = AB² + BC² + CD²

Now, AB is the height, h, BC is the breadth, b and CD is the length l. Hence, we can write

AD² = h² + b² + l²

Or, AD² = l² + b² + h²

Hence,

$AD = \sqrt{l^2 + b^2 + h^2}$

Hence proved.

$\rule{200}{2}$

Answer 2

Let the length and breadth  and height of the cuboid be "l" and "b" and "h" respectively

Length of diagonal :-

√l² + b² + h²