Question

Bricks are delivered to a work site and stacked in rows and columns, forming a rectangular prism. The length of the prism is 3 feet greater than its width, and its height is 1 foot less than its width. Find the dimensions of the prism formed by the bricks, given that its volume is 1170 cubic feet. I have the answer but apparently guessing and checking dosent count as solving.

Answer 1

Answer:
length of prism = 13 ft
width of prism = 10 ft
height of prism = 9 ft

Step-by-step explanation:
Assume the the width of the prism is w
We are given that:
1- the length is 3 ft greater than the width
This means that: length = w + 3
2- the height is 1 ft less than than the width
This means that: height = w - 1

Now, we have the volume = 1170 ft³
volume of rectangular prism = length * width * height

Substitute with the givens in the equation and solve for w as follows:
1170 = (w+3)*(w)*(w-1)
1170 = w(w+3)(w-1)
1170 = (w²+3w)(w-1)
1170 = w³ - w² + 3w² - 3w
1170 = w³ + 2w² - 3w
w³ + 2w² - 3w - 1170 = 0
Factoring the above expression, we would find that:
either w = 10 ft .........> accepted solution
or w = -6 + 9i .......> rejected as side length cannot be imaginary
or w = -6 - 9i ..........> again rejected as side length cannot be imaginary

This means that:
width of prism = 10 ft

Now, we can get the other two dimensions as follows:
length = w + 3= 10 + 3 = 13 ft
height = w - 1 = 10 - 1 = 9 ft

Hope this helps :)