Solve the problem.
-A farmer has 800 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A?
A) $A ( x ) = - x ^ { 2 } + 400 x ; \{ x \mid 0

Question

Solve the problem.
-A farmer has 800 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A? 
A) $A ( x ) = - x ^ { 2 } + 400 x ; \{ x \mid 0 < x < 800 \}$
B) $A ( x ) = - x ^ { 2 } + 400 x ; \{ x \mid 0 < x < 400 \}$
C) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 800 \}$
D) $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 400 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 400 \}$

Quizplus · Accepted Answer

The total perimeter is 800 yards, so if x is the width, the length would be $400 - x$ (since $2x + 2(400 - x) = 800$). The area $A(x)$ is $x(400 - x) = 400x - x^2$. The domain is $0 < x < 400$ because the width must be less than half the total perimeter for a rectangle to be formed.

Solve the Problem A(x)=−x2+400x;{x∣0<x<800}A ( x ) = - x ^ { 2 } + 400 x ; \{ x \mid 0 < x < 800 \}A(x)=−x2+400x;{x∣0<x<800}

Solve the Problem $A ( x ) = - x ^ { 2 } + 400 x ; \{ x \mid 0 < x < 800 \}$