Question

11:10:2 What is the length,breadth and height of the cuboid, if its body diagonal is 30cm long?

Answer 1

Answer:

Length =22 cm

Breadth = 20 cm

Height = 4 cm

Step-by-step explanation:

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

Given:

l:b:h=11:10:2

Then,

l=11k

b=10k

h=2k

Also, Length of the diagonal = 30 cm

$\bold{\sqrt{l^2+b^2+h^2}=30}$

$\implies\:\sqrt{(11k)^2+(10k)^2+(2k)^2}=30$

$\implies\:\sqrt{(121k^2+100k^2+4k^2}=30$

$\implies\:\sqrt{225k^2}=30$

$\implies\:15k=30$

$\implies\:k=2$

Therefore, the dimension of the cuboid are

l=11(2)=22 cm

b=10(2)=20cm

h=2(2)= 4 cm