The formula for finding the volume of a rectangular prism is V = lwh. The height h of a rectangular prism is 12 centimeters. The prism has a volume of 10,800 cubic centimeters. The prism's length l is modeled by 3x centimeters and its width w by (2x + 1) centimeters. What is the value of x? What are the dimensions of the length and the width?

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

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