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

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

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

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