The volume of a box (V) varies directly with its length (l). If a box in the group has a length of 30 inches, and the girth of 20 inches (perimeter of the side formed by the width and height), what is its height? Use k = 24. (Hint: Volume = length width height. Solve for length, and substitute into the equation for constant of proportionality.) ___ inches or ___ inches

Given:

length 30 inches

k = 24

v = l * w * h

volume varies directly w / the length: v = kl

v = 24 * 30 = 720

k = wh

24 = wh

w = 24/h or h = 24/w

P = 2w + 2h

20 = 2w + 2h

20 = 2 (24/h) + 2h

20 = 48/h + 2h

48/h + 2h - 20 = 0

h (48/h + 2h - 20) = 0

48 + 2h² - 20h = 0

2h² - 20h + 48 = 0

2 (h² - 10h + 24) = 0

2 (h - 6) (h - 4) = 0

h = 6 or h = 4

Since the height serves as the length in the perimeter equation, then its measure is 6 and width is 4.

length = 30; width = 4; height = 6.