Question

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

Answer 1

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.