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Gerardo is constructing a box. The height of the box is h feet. The width of the box is four feet more than three times its height. The width can be expressed as The length of the box is four feet less than two times its height. The length can be expressed as The area of the base of the box is the product of its width and length. The area of the base of the box Gerardo is constructing can be expressed *in factored form* as The above expression for area can be *expanded* to

Gerardo is constructing a box. The height of the box is h feet. The width of the box is four feet more than three times its height. The width can be expressed as The length of the box is four feet less than two times its height. The length can be expressed as The area of the base of the box is the product of its width and length. The area of the base of the box Gerardo is constructing can be expressed *in factored form* as The above expression for area can be *expanded* to

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Description:** Gerardo is constructing a box. The height of the box is \( h \) feet. 1. **Width of the Box:** - The width of the box is four feet more than three times its height. - **Expression for width:** \( 3h + 4 \) 2. **Length of the Box:** - The length of the box is four feet less than two times its height. - **Expression for length:** \( 2h - 4 \) 3. **Area of the Base:** - The area of the base of the box is the product of its width and length. - **Factored expression for area:** \( (3h + 4)(2h - 4) \) 4. **Expanded Expression for Area:** - The area expression can be expanded to: \( 6h^2 - 12h + 8h - 16 = 6h^2 - 4h - 16 \) This setup allows students to practice creating and manipulating algebraic expressions based on word problems, emphasizing the importance of understanding relationships between geometric dimensions and algebraic expressions.
Transcribed Image Text:**Problem Description:** Gerardo is constructing a box. The height of the box is \( h \) feet. 1. **Width of the Box:** - The width of the box is four feet more than three times its height. - **Expression for width:** \( 3h + 4 \) 2. **Length of the Box:** - The length of the box is four feet less than two times its height. - **Expression for length:** \( 2h - 4 \) 3. **Area of the Base:** - The area of the base of the box is the product of its width and length. - **Factored expression for area:** \( (3h + 4)(2h - 4) \) 4. **Expanded Expression for Area:** - The area expression can be expanded to: \( 6h^2 - 12h + 8h - 16 = 6h^2 - 4h - 16 \) This setup allows students to practice creating and manipulating algebraic expressions based on word problems, emphasizing the importance of understanding relationships between geometric dimensions and algebraic expressions.
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