Question

The length of a rectangular prism is four times its width. the volume of the prism is 380 cubic meters. find the length and width of the prism

Answer 1

Answer:

The length and width of the prism are 20 metres and 5 metres respectively

Step-by-step explanation: given that the length of a rectangular prism is four times its width. That is

Length L = 4 width W

L = 4W

the volume of the prism is 380 cubic meters

V = L × W × H

380 = 4W × W × H

380 = 4W^2H

W^2H = 380/4

W^2 H = 95

The only way to get a perfect square number is to make H = 3.8

3.8W^2 = 95

W^2 = 95/3.8

W^2 = 25

W = 5

But L = 4W

L = 4 × 5 = 20

The length and width of the prism are therefore 20 metres and 5 metres respectively

Answer 2

Answer:

Length = 20m

Width = 5m

Step-by-step explanation:

Volume of a rectangular prism = Length × Width × Height

V = LWH ... 1

If the length of the rectangular prism is four times its width, this is expressed as:

L = 4W ... 2

Volume = 380m³

Substituting equation 2 and the volume of into the formula, we have:

380 = (4W)WH

380 = 4W²H

W²H = 380/4

W²H = 95

W² = 95/H

W = √95/H

Since we are not given the height of the prism, we need to assume a value for Height that will make the width a perfect square.

Taking H = 3.8m

W = √95/3.8

W = √25

W = 5m

Width = 5m

Since L = 4W

Length of the prism = 4(5)

Length of the prism = 20m