18
QuizMultiple Choice

Modeling with Quadratic Equations — Quiz

Question 18 • Algebra II

The Davidson family wants to expand its rectangular patio, which currently measures 15 feet by 12 feet They want to extend the length and width the same amount to increase the total area of the patio by 160 ft squared Which quadratic equation best models the situation? cap A is equal to l w

Answer
A
15 x times 12 x is equal to 15 times 12 plus 160
B
2 times open paren 15 plus x close paren plus 2 times open paren 12 plus x close paren is equal to 15 times 12 plus 160
C
open paren 15 plus x close paren times open paren 12 plus x close paren is equal to 15 times 12 plus 160
D
15 times 12 plus x times x is equal to 15 times 12 plus 160

Explanation

Let x be the number of feet added to both the length and width. The new dimensions are 15 + x feet and 12 + x feet, so the new area is (15 + x)(12 + x). The area increases by 160 square feet, making the new area equal to the original area, 15 × 12, plus 160. Thus choice D, (15 + x)(12 + x) = 15 × 12 + 160, models the situation.

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