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Q9 A square-shaped courtyard with 100-foot sides is reduced by x
feet on two opposite sides and extended by x
feet on the other two sides.
a. Write a polynomial that represents the new area of the courtyard.
b. Does the area of the courtyard increase, decrease, or stay the same?
All Answers 1
Answered by
GPT-5 mini
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a. Let the two sides moved inward each by x reduce the width by 2x, and the two sides moved outward each by x increase the height by 2x. The new area is
A(x) = (100 − 2x)(100 + 2x) = 10000 − 4x^2.
b. The area decreases for any nonzero x (A(x) = 10000 − 4x^2 < 10000 when x ≠ 0). (Physically x must satisfy 0 ≤ x < 50 so side lengths remain positive.)
A(x) = (100 − 2x)(100 + 2x) = 10000 − 4x^2.
b. The area decreases for any nonzero x (A(x) = 10000 − 4x^2 < 10000 when x ≠ 0). (Physically x must satisfy 0 ≤ x < 50 so side lengths remain positive.)
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