Question

volume of rectangular room 60 and its diagonal 5√2 if height of the room is 3m then length and breadth

Answer 1

Answer:

The length and breadth are 4 and 5.

Step-by-step explanation:

The volume of a rectangle is 60 metre cube.

Volume of a cuboid is

Volume=l\times b\times hVolume=l×b×h

where, l is length and b is breadth and h is height.

Height of the room is 3 metre.

60=l\times b\times 360=l×b×3

20=l\times b20=l×b

\dfrac{20}{b}=l

b

20

=l ... (1)

Length of the digonal is

lenght^2=l^2+b^2+h^2lenght

2

=l

2

+b

2

+h

2

diagonal is 5 root 2.

(5\sqrt{2})^2=l^2+b^2+3^2(5

2

)

2

=l

2

+b

2

+3

2

50=l^2+b^2+950=l

2

+b

2

+9

41=l^2+b^241=l

2

+b

2

.... (2)

On solving (1) and (2) we get

l=5,4,-5,-4l=5,4,−5,−4

Dimensions can not be negative.

If l=5, then b=4.

If l=4, then b=5.

Therefore, the length and breadth are 4 and 5.