Bricks are delivered to a work site and stacked in rows and columns, forming a rectangular prism. The length of the prism is 3 f
eet 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 set it up, and I've tried solving it, and this is all I have so far. If you could help me out by completing it AND explaining so I can better understand it, that would be great!)
Here's what I have so far:
W= x, L= x+3, H= x-1
Volume= 1170 ft^3, so L*W*H= 1170 ft^3
(x+3)*x*(x-1) (after this is where I get stuck)
10 points to whoever answers correctly! Thank you for your time!!!
(I set it up, and I've tried solving it, and this is all I have so far. If you could help me out by completing it AND explaining so I can better understand it, that would be great!)
Here's what I have so far:
W= x, L= x+3, H= x-1
Volume= 1170 ft^3, so L*W*H= 1170 ft^3
(x+3)*x*(x-1) (after this is where I get stuck)
10 points to whoever answers correctly! Thank you for your time!!!
1 answer:
Correct so far. Finish up.
.. (x +3)(x)(x -1) = 1170
.. x^3 +2x^2 -3x -1170 = 0 . . . . . . one sign change ⇒ one positive real solution
This is a cubic equation with one positive real solution. There are several possible approaches to solving this. My favorite is to let a graphing calculator show me the solution.
You can also factor 1170 = 13*10*9, so x=10.
The width of the prism is 10 feet; the length is 13 feet; the height is 9 feet.
.. (x +3)(x)(x -1) = 1170
.. x^3 +2x^2 -3x -1170 = 0 . . . . . . one sign change ⇒ one positive real solution
This is a cubic equation with one positive real solution. There are several possible approaches to solving this. My favorite is to let a graphing calculator show me the solution.
You can also factor 1170 = 13*10*9, so x=10.
The width of the prism is 10 feet; the length is 13 feet; the height is 9 feet.
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