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 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

ajeigbeibraheem ajeigbeibraheem · Answer 2 · 2022-03-24T12:41:26+01:00

The height of the the travel version box shows that it's 1.125cm tall.

What are word problems?

Word problems in mathematical applications involves the use of arithmetic operations, fractions, variables and with crucial understanding of the problem.

In this given question, let's assume that:

The height of the game box h1 = 8cm
Area of the plastic wrap A1 = 1408 sq.cm

However, if a travel version is produced with:

An area plastic of A2 = 198 sq.cm

Then, the height of the travel version showing how tall it is can be computed as follows:

[tex]\mathbf{H_2 = \dfrac{8cm \times 198 \sq.cm}{1408 \ sq.cm} }[\tex]

[tex]\mathbf{H_2 = 1.125 cm }[\tex]

Thus, the height of the travel version is 1.125cm tall.

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