In the given problem, apply your knowledge in algebraic expression specially in mathematical operation and solving unknown variables.
Formula or finding volume of rectangular prism is L×W×H.
Assume that the cage is a rectangular prism, since there are three given dimensions (lenght, width and height).
height = (3x – 4) feet,
length = (x + 3) feet,
width = (x + 1) feet.
Volume = 120 cubic feet
120 = (x+3)(x+1)(3x-4)
120 = (3x-4)(x²+4x+3)
120 = (3x³+12x²+9x-4x²-16x-12)
120 = 3x³ + 8x - 7x - 12
3x³ + 8x - 7x - 132 = 0
3x³ + 8x - 7x - 132 = 0
x = 3 | 3x³ + 8x - 7x - 132 = 0
3 | 3 | 8 | -7 | -132
| | 9 | 51 | 132
| 3 | 17 | 44 | 0
Therefore, x = 3
height = (3x – 4) feet, → 3(3) - 4 = 5 feet
length = (x + 3) feet, → 3+3 = 6 feet
width = (x + 1) feet. → 3+1 = 4 feet
Volume = lwh
120 = (5)(6)(4)
120 = 120 ✓
Learn more about the formula for volume of different figures here at https://brainly.ph/question/274699
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