College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.2 - Applications and Modeling with Linear Equations - 1.2 Exercises: 17

Answer

The height of the box is 4 feet.

Work Step by Step

We know that the box has 6 faces. The surface area of the box, 496 ft^{2} is equal to the sum of the areas of each of the 6 faces. All faces are rectangular, so the area of a face is equal to the product of its two sides. Therefore, the top and bottom faces have an area of 18*8=144, the end faces have an area of 8h, and the remaining two faces have a length of 18h. Adding the areas of all the faces to equal the total surface area of 496 feet squared, this situation can be modeled by the equation 2*144+2*8h+2*18h=496, remembering that each face has an adjacent opposite face. Solving for h in the equation: 2*144+2*8h+2*18h=496. 144+8h+18h=248. Divide both sides by 2 144+26h=248. Combine like terms 26h=104 Subtract 144 from both sides h=4 Divide both sides by 26. Therefore, the height of the box is 4 feet.
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