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:

The volume of a rectangular prism is  

V = l · w · h

V= 252 cm3

h= 3 cm

l=5+W

W=x then l=5+x

V=(5+x)*x*3=252

3x^2+15x=252 cm3

the equation that models the volume of the tray in terms of its width, x, in centimeters.

3x^2 +15x=252 cm3

for width=7.5 cm

3x^2 +15x=3*(7.5) ^2+15*7.5= 281.25 cm3

281.25>252  

it is not possible that the width is 7.5 cms

Step-by-step explanation:

Answer 2

Answer:

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.

3x2 + 15x = 252

Is it possible for the width of the tray to be 7.5 centimeters?

no it is too large

Step-by-step explanation: