Question

Find the length of the diagonal of a cuboid with the length 10 cm breath 8 cm and height =4 cm​

Answer 1

$\sf{Answer}$

Step-by-step-explanation:-

Given :-

• Length of cuboid = 10cm
• Breadth of cuboid = 8cm
• Height of cuboid = 4cm

To find :-

Diagonal of a cuboid

Formula implemented :-

Diagonal of cuboid = $\sf\sqrt{(l)²+ (b)² + (h)²}$

Solution:-

By the above formula we can find diagonal of cuboid

So,

Diagonal of cuboid = $\sf\sqrt{(l)² +( b)² + (h)²}$

Diagonal of cuboid = $\sf\sqrt{(10)² + (8)² + (4)²}$

Diagonal of cuboid = $\sf\sqrt{100+64+16}$

Diagonal of cuboid = $\sf\sqrt{180}$

It can be simplified as

$\sf\sqrt{180}$

= $\sf\sqrt{(2) (2) (45)}$

= $\sf\sqrt{(2)² (45)}$

= $\sf\sqrt{(2)²}$ $\sf\sqrt{45}$

$\sf{2}$ $\sf\sqrt{(3)(5)(3)}$

$\sf{2}$ $\sf\sqrt{(3)² (5)}$

$\sf{2}$ $\sf\sqrt{(3)²}$ $\sf\sqrt{5}$

$\sf{2}$ × $\sf{3}$ × $\sf\sqrt{5}$

6 $\sf\sqrt{5}$

So, diagonal of cuboid is 6 $\sf\sqrt{5}$