A board game manufacturer wraps its game boxes in plastic. It's most popular game comes in a box that's 8cm tall and uses 1408 square centimeters of plastic wrap. The company sells a travel version of the game in a box thats a dilation of the original box. The travel version uses 198 square centimeters of plastic wrap. How tall is the travel versions box?

The travel version box is 1.125 cm tall.

Explanation:

The relationship between the height of the box and the area of the plastic wrap is direct in which increase in one quantity leads to a corresponding increase in the other quantity and vice versa.

Let h1 and A1 represent the height and area of plastic wrap of the original box

Let h2 and A2 represent the height and area of plastic wrap of the travel version box.

h varies directly as A

h/A = constant

h1/A1 = h2/A2

h2 = h1A2/A1

h1 = 8 cm

A1 = 1408 cm^2

A2 = 198 cm^2

h2 = 8 × 198/1408 = 1.125 cm

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