Can't figure this one out. A homeowner wants to fence a rectangular garden using 150 ft of fencing....?

Question

A homeowner wants to fence a rectangular garden using 150 ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.

Note: Its basically using maximum funciton where the maximum function value occurs at the vertex of the graph of the function.

Answer 1

Let X = long side of garden; Let Y=short side of garden.

Maximum area occurs when X = 2Y.

Perimeter = 150 = X + 2*Y = 4 * Y

Therefore Y = 150 / 4 = 37.5 ... and X = 2*Y = 75

Maximum area = 75 * 37.5 = 2812.5 ft2

Answer 2

i'm uncertain what you're asking. If one element of a rectangle (all indoors angles are ninety°) is the storage with an unknown length and something of the fringe equals 150 feet, you desire to appreciate the size that provide you the biggest section interior the rectangle? if so, then the optimum section may be contained interior a sq., so the element of the storage might might desire to be 50 feet and the three remaining factors might additionally be 50 feet slightly. the section might then be 50 feet x 50 feet = 2500 feet²

Answer 3

2x + y =150
Maximize x * y

A rectangle's area is maximized where the sides are equal.

3x = 150
x,y = 50

Answer 4

x=one side
y=other side parallel to garage
2x+y=150
x*y=f
f'=150-2x-2x=0 -->x=37.5 & y=75
f=2812.5