Question

1. Fatimah wants to put a rectangular garden on her property using 72 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.)  
(a) Let x represent the length of the side of the rectangle along the river. Express the garden's area as a
function of x
(b) Find the maximum area. SHOW WORK.
(c) Find the dimensions of the rectangle of maximum area

Answer 1

this is the answer I got
a.) A(x)=-2x^2 +72x
b.) A(x)= -2(18)^2+72(18)=648m squared
c.) 72-2(18)=36
648 by 36
but im not sure if it is correct or not

Answer 2

The length of the rest of the fence totals length (72 - x) meters, divided up evenly between the two sides perpendicular to the river.
The width3 is (36 - x/2), so the area of the garden is x((36 - x/2) = 36x - x^2/2.

Answer 3

The x-coordinate of the parabola y = 36x - x^2 is -36/(1*(-1/2) = 36.
That's the length of the field. Its width is 36 - 36/2 = 18 meters.
The area es 36*18 m^2 = 646 m^2.

Answer 4

648 m^2.

Answer 5

soo i was right? right