Solve the problem.
-Sue wants to put a rectangular garden on her property using 70 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) $A ( x ) = 35 x - \frac { 1 } { 2 } x ^ { 2 }$
B) $A ( x ) = 34 x - \frac { 1 } { 4 } x ^ { 2 }$
C) $A ( x ) = 35 x ^ { 2 } - x$
D) $A ( x ) = 36 x - 2 x ^ { 2 }$

Question

Solve the problem.
-Sue wants to put a rectangular garden on her property using 70 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) $A ( x ) = 35 x - \frac { 1 } { 2 } x ^ { 2 }$
B) $A ( x ) = 34 x - \frac { 1 } { 4 } x ^ { 2 }$
C) $A ( x ) = 35 x ^ { 2 } - x$
D) $A ( x ) = 36 x - 2 x ^ { 2 }$

Quizplus · Accepted Answer

The total fencing available is 70 meters, and since the river acts as one side of the rectangle, only three sides need fencing. If x is the length of the side along the river, the remaining fencing, 70 meters, will be used for the other two sides and the side opposite the river. Let y be the length of the other two sides, so we have $2y + x = 70$, which simplifies to $y = \frac{70 - x}{2}$. The area of the rectangle, $A(x)$, is given by $x \times y$, which becomes $x \times \frac{70 - x}{2} = 35x - \frac{1}{2}x^2$.

Solve the Problem A(x)=35x−12x2A ( x ) = 35 x - \frac { 1 } { 2 } x ^ { 2 }A(x)=35x−21​x2

Solve the Problem $A ( x ) = 35 x - \frac { 1 } { 2 } x ^ { 2 }$