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

Answer:

length is 28.86ft

width= 4.12ft

Step-by-step 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

$w^{2}= \frac{595}{35\\} \\w^{2}= 17$

find the square root of both sides we have

$w=\sqrt{17} \\w= 4.12$

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

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