Question

The breadth of a room is twice its height and half its lenghth and its volume is 1000m^.its dimension are

Answer 1

Answer:

Legnth = 20 m , Breadth = 10 m

Height = 5 m

Step-by-step explanation:

Given--->

----------

Breadth of room is twice of its height

and breadth of room is half of its length

and volume of room is 1000 m³

To find----> Dimensions of room

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Solution--->

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Let length of room be x m

Breadth of room = (1/2) length

= (1/2) x

= (x / 2)

Height of room = (1 / 2 ) breadth

=( 1 / 2 ) (x / 2)

= ( x / 4 )

Volume of room = length × breadth ×

height

1000 = x ( x / 2 ) ( x / 4 )

1000 = x³ / 8

x³ = 8 × 1000

x³ = 8000

x³ = 20 × 20 × 20

x³ = ( 20 ) ³

Taking cube root of both sides

X = 20

Length = x = 20 m

Breadth = x / 2 = 20 / 2 = 10 m

Height = x / 4 = 20 / 4 = 5 m

Answer 2

Answer:

To find such type of questions fastly let the smallest side be equals x so that other sides will not be in fraction form so it will be easier to solve it.

SOLUTION:-)

Let Height of the room be(H) = x.

So, ATQ)

Breadth of the room will be(B)= 2x.

and

length of room will be(L) = 4x.

As,

Volume of a room is given by

VOLUME = L × B × H.

Given that volume of the room is 1000cubic m.

So,

$4x \times 2x \times x = 1000 {m}^{3} \\ \\ 8 {x}^{3} = 1000 \\ \\ {x}^{3} = \frac{1000}{8} \\ \\ {x}^{3} = 125 \\ \\ x = \sqrt[3]{125} \\ \\ x \sqrt[3]{5 \times 5 \times 5} \\ \\ x = 5m$

Now,

length of room = 4x = 4 x 5 = 20m.

breath of room = 2x = 2 x 5 = 10m.

height of room = x = 5m.

So,

dimensions of room will be 20m x 10m x 5m.