A rectangular garden has a perimeter of 40 meters. The... | SAT Nonlinear functions Question, Answer Explained

Math · Advanced MathMedium

A rectangular garden has a perimeter of $40$ meters. The function $A(w) = w(20 - w)$ gives the area, in square meters, of the garden when its width is $w$ meters. What is the maximum possible area, in square meters, of the garden?

$10$

$20$

$100$

$400$

Show answer and explanation

Answer: C

The graph of $A(w) = w(20 - w)$ is a parabola that opens downward with zeros at $w = 0$ and $w = 20$ . The maximum occurs halfway between the zeros, at $w = 10$ . The maximum area is $A(10) = 10(10) = 100$ square meters.

Choice A is the width that gives the maximum area, not the maximum area itself.

Why the other choices are wrong

A. 10 meters is the width that gives the greatest area. The area at that width is 10 × 10 = 100.
B. A width of 20 leaves a length of 0, so the area is 0, not the maximum.
D. 400 is 20². The length and width add to 20, so the area is at most 10 × 10.

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