Question

Sue wants to put a rectangular garden on her property using 88 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. what is the largest area that can be enclosed?

Answer 1

Area = 44x - x²/2

Explanation:

Given that:

Meter of fencing = 88m

Length of side of rectangle along the river = x

Only one more length is needed since river as been used as one side length of the fence.

Length = x

Width of rectangle = y = 2y (for both sides)

Hence ;

x + 2y = 88 meters

Expressing in terms of y

2y = 88 - x

y = (88 - x) / 2

y = 44 - x/2

Area of rectangle = Length * width

Area = x * y

Area = x * (44 - x/2)

Area = 44x - x²/2

Maximum. Area :

Perimeter = 4s

88 = 4s

s = 88/4 = 22

x = 2(22) = 44 = Length ; y = 22 = width

Maximum area = (22 * 44) = 968m²