Question

(e) What will be the length of diagonal in a room with dimensions 10 cm x 12
cm x 8 cm.
Ans. 2 under root 77 cm.​

Answer 1

Diagonal length = 2√77 cm.

Step-by-step explanation:

Use the formula of longest diagonal of a cuboid =

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

Here, l = 10 cm, b = 12 cm and h = 8 cm

Therefore, length of the diagonal =

$\sqrt{ {10}^{2} + {12}^{2} + {8}^{2} } \\ = \sqrt{100 + 144 + 64} \\ = \sqrt{308} \\ = \sqrt{4 \times 77} \\ = 2 \sqrt{77}$

Hence, the diagonal length = 2√77 cm.