Question

Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width. The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height. Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.

Answer 1

Answer:

$3x^2 + 15x - 252 = 0$

Step-by-step explanation:

The volume of the prism is 252 cubic centimeters.

The volume of a rectangular prism is gotten by the formula:

V = l * w * h

where l = length

w = width

h = height

The height of the prism is 3 cm.

Let x be the width of the prism.

The length of the prism is 5 cm longer than the width.That is:

l = 5 + x

The volume of the prism is therefore:

V = (5 + x) * x * 3

$=> 252 = (5x + x^2) * 3\\\\252 = 15x + 3x^2\\\\=> 3x^2 + 15x - 252 = 0$

This is the equation that models the volume of the tray in terms of x.