Question

Select the correct answer from each drop-down menu. 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. 5 x2 + 3 x = 252 Is it possible for the width of the tray to be 7.5 centimeters?

Answer 1

Answer:

w = 7 cm

Step-by-step explanation:

Volume = 252 cm³

Height, h = 3cm

Let width = w

Length, l = w + 5

Volume of rectangular prism, V = l * w * h

252 = (w + 5) * w * 3

252 = (w + 5) * 3w

252 = 3w² + 15w

3w² + 15w - 252 = 0

w² + 5w - 84 = 0

w² + 12w - 7w - 84 = 0

w(w + 12) - 7(w + 12) = 0

(w + 12) = 0 or (w - 7) = 0

w = - 12 or w = 7

w cannot be negative

Hence, w = 7 cm