Question 5 Answer & Explanation - SAT Advanced Math

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advanced-math

A rectangle has perimeter 20. Let $x$ be the width. Express the area $A$ as a function of $x$ and find the domain.

$A(x) = 10x - x^2$ , $0 < x < 10$

$A(x) = 20x - x^2$ , $0 < x < 20$

$A(x) = 10x - x^2$ , $x > 0$

$A(x) = x^2 + 10x$ , $0 < x < 10$

Choice A is the correct answer.

Perimeter $2x + 2l = 20 \Rightarrow x + l = 10 \Rightarrow l = 10 - x$ .
Area $A(x) = x(10 - x) = 10x - x^2$ .
Domain: Width $x > 0$ and Length $10 - x > 0 \Rightarrow x < 10$ . So $0 < x < 10$ .

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

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