Question

A storage space in a basement is in the shape of a rectangular prisim. The hieght of the storage space is 5 feet. The length is seven times the width. The volume of the storage space is 595 cubic feet. Find the width and length of storage space

Answer 1

length is 28.86ft

width= 4.12ft

Explanation:

This problem bothers on the mensuration of solid shapes, a rectangular prism.

The storage space takes the shape of a rectangular prism, and we are required to find the width and length of the storage space.

let the width of the basement be "w"

Given data

volume v=
`595ft^(3)`

length l =
`7w ft`

width w=
`w`

height h=
`5 ft`

We know that the expression for the volume of a rectangular prism is

`volume= length * width* height`

substituting our data we have to find "w"

`595= 7w*w*5\\595=7w^(2)*5\\ 595= 35w^(2) \\`

dividing both sides by 35 we have

`w^(2)= (595)/(35\\) \\w^(2)= 17\\`

find the square root of both sides we have

`w=√(17) \\w= 4.12`

since we know that length= 7w and width = w , we can substitute our value for w and find the length and width

`length= 7*4.12= 28.86ft\\width = 4.12ft`