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

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

40 x 50 = 2000

step-by-step explanation: