Answer:
x = 12
prism's length = 36 centimeters
Prisms width = 25 centimeters
Step-by-step explanation:
volume of a rectangular prism, V = length × width × height
volume = 10,800 cubic centimeters
prism's length = 3x
Prisms height = 12 centimeters
Prisms width = (2x + 1)
volume of a rectangular prism, V = length × width × height
10,800 = 3x * 2x + 1 * 12
10,800 = 6x² + 3x * 12
10,800 = 72x² + 36x
72x² + 36x - 10,800 = 0
2x² + x - 300 = 0
Using quadratic formula
x = -b ± √b² - 4ac / 2a
= -1 ± √1² - 4*2*-300 / 2*2
= -1 ± √1 - (-2400) / 4
= -1 ± √1 + 2400 / 4
= -1 ± √2401 / 4
= -1 ± 49 / 4
x = (-1 + 49)/4 or (-1 - 49)/4
= 48/4 or -50/4
x = 12 or -12.5
x cannot be a negative value
Therefore, x = 12
prism's length = 3x
= 3(12)
= 36 centimeters
prism's length = 36 centimeters
Prisms width = (2x + 1)
= 2(12) + 1
= 24 + 1
= 25 centimeters
Prisms width = 25 centimeters
