Question

The length of a room is twice the width and three times its height. If the volume of the room is 288 metre cube find the length of the room

Answer 1

The Length of the room is 12 meters  .

Step-by-step explanation:

Given as :

Statement I

The length of a room is twice the width

Let The length of room = L meters

Let The width of room = W meters

Let The height of room = H meters

So,

Length = 2 width

i.e  L = 2 W                      .....................1

Again

Statement II

The length of a room is  three times its height

Length = 3 Height

i.e  L = 3 H                    ...................2

The volume of the room = v = 288 meters cube

∵ volume of the room = Length × Width × Height

Or,                              v = L × W × H

Or,                              v = L × $\dfrac{L}{2}$ × $\dfrac{L}{3}$

Or,                     288 m³ = $\dfrac{L^{3} }{6}$

Or,                             L³ = 288 × 6

Or,                             L³ = 1728

∴                                L = ∛1728

i.e                     Length = 12 meters

So, The Length of the room = L = 12 meters

Hence,  The Length of the room is 12 meters  . Answer

Answer 2

Answer:

Volume(V) = Length(L) x Width(W) x Height(H)

Given: L = 2W , L = 3H, and V = 288 cc

L = 2W ;==> W = L/2 and L = 3H ;==>H = L/3

288 = L x (L/2) x (L/3)

288 = L 3 /6

L 3 = 1728

L = 12 cm

W = 12/2,==> W = 6 cm

H = 12/3,==> H = 4 cm

>>>>>>>>> Length = 12 cm, Width = 6 cm, and Height = 4 cm