Solve.
-Sue wants to put a rectangular garden on her property using 66 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as One side of the rectangle. (Fencing is then needed only on the other three sides.)Let x represent the length of the side of the rectangle along the river. Express the garden's area as a function of x.
A) $A ( x ) = 32 x - \frac { 1 } { 4 } x ^ { 2 }$
B) $A ( x ) = 33 x - \frac { 1 } { 2 } x ^ { 2 }$
C) $A ( x ) = 33 x ^ { 2 } - x$
D) $A ( x ) = 34 x - 2 x ^ { 2 }$

Question

Solve.
-Sue wants to put a rectangular garden on her property using 66 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as One side of the rectangle. (Fencing is then needed only on the other three sides.)Let x represent the length of the side of the rectangle along the river. Express the garden's area as a function of x. 
A) $A ( x ) = 32 x - \frac { 1 } { 4 } x ^ { 2 }$
B) $A ( x ) = 33 x - \frac { 1 } { 2 } x ^ { 2 }$
C) $A ( x ) = 33 x ^ { 2 } - x$
D) $A ( x ) = 34 x - 2 x ^ { 2 }$

Quizplus · Accepted Answer

Since the total fencing available is 66 meters and one side (the length along the river) doesn't require fencing, the perimeter equation using the remaining fencing is $2w + x = 66$, where $w$ is the width of the rectangle. Solving for $w$, we get $w = \frac{66 - x}{2}$. The area of the rectangle, $A$, is given by $A = x \cdot w$. Substituting $w$ from the equation above, we get $A(x) = x \cdot \left(\frac{66 - x}{2}\right) = 33x - \frac{1}{2}x^2$, which matches choice B.

Solve -Sue Wants to Put a Rectangular Garden on Her A(x)=32x−14x2A ( x ) = 32 x - \frac { 1 } { 4 } x ^ { 2 }A(x)=32x−41​x2

Solve
-Sue Wants to Put a Rectangular Garden on Her $A ( x ) = 32 x - \frac { 1 } { 4 } x ^ { 2 }$