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

No, too large

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

Step-by-step explanation:

full plato answer verified correct

Answer 2

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