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=[tex]595ft^{3}[/tex]
length l = [tex]7w ft[/tex]
width w= [tex]w[/tex]
height h= [tex]5 ft[/tex]
We know that the expression for the volume of a rectangular prism is
[tex]volume= length * width* height[/tex]
substituting our data we have to find "w"
[tex]595= 7w*w*5\\595=7w^{2}*5\\ 595= 35w^{2} \\[/tex]
dividing both sides by 35 we have
[tex]w^{2}= \frac{595}{35\\} \\w^{2}= 17\\[/tex]
find the square root of both sides we have
[tex]w=\sqrt{17} \\w= 4.12[/tex]
since we know that length= 7w and width = w , we can substitute our value for w and find the length and width
[tex]length= 7*4.12= 28.86ft\\width = 4.12ft[/tex]
