A homeowner has $360 to spend on building a fence around a rectangular garden. Three sides of the fence will be constructed with wire fencing at a cost of $2 per foot. The fourth side is to be constructed with wood fencing at a cost of $6 per foot. Find the dimensions of the rectangle that will maximize the area of the rectangle.

The width is 22.5 feet and the length 45 feet.

Step-by-step explanation:

Let l represent the length of the rectangle and  w represent the width of the rectangle. The cost of the fence (C) is:

C = 2l + 2w + 2l + 6w

C = 4l + 8w

360 = 4l + 8w

360 = 4(l + 2w)

90 = l + 2w

l = 90 - 2w

Area (A) of rectangle = length * width

A = l * w

Put l = 90 - 2w

A = (90 - 2w)w

A = 90w - 2w²

The maximum area is at A' = 0, hence:

Differentiating gives:

A' = 90 - 4w

Put A' = 0

0 = 90 - 4w

4w = 90

w = 22.5 feet

l = 90 - 2w = 90 - 2(22.5) = 45 feet

Hence the width is 22.5 feet and the length 45 feet.

if x = 1, then the answer is 3.5

step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

radha is now 5 years old

3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

hope this !