Question

the dimensions of a cuboid are in the ratio 11:10:2. what is the Length, breadth and height of the cuboid, if its body diagonal is 30 cm long.

Answer 1

Step-by-step explanation:

11x:10x:2x

diagonal=(l^2+b^2+h^2)^1/2 = 30

(121xx+100xx+4xx)^1/2

(225xx)^1/2

15x=30

x=2

length =11x=22

breadth= 10x= 20

hight= 2x=4

Answer 2

Answer:

Length, breadth and height of the cuboid is 22,20 and 4 respectively.          

Step-by-step explanation:

Given :  The dimensions of a cuboid are in the ratio 11:10:2. if its body diagonal is 30 cm long.

To find : What is the Length, breadth and height of the cuboid?

Solution :

Let the ratio divides be 'x'.

So, L : B : H = 11: 10: 2 beca,e

L=11x

B=10x

H=2x

We know, The diagonal formula of cuboid is given by

$D=\sqrt{L^2+B^2+H^2}$

Substituting the values,

$30=\sqrt{(11x)^2+(10x)^2+(2x)^2}$

$30=\sqrt{121x^2+100x^2+4x^2}$

$30=\sqrt{225x^2}$

$30=\sqrt{(15x)^2}$

$30=15x$

$x=\frac{30}{15}$

$x=2$

So, The dimension became

L=11x=11(2)=22

B=10x=10(2)=20

H=2x=2(2)=4

Therefore, Length, breadth and height of the cuboid is 22,20 and 4 respectively.