Respuesta :
Answer:
90 feet
Explanation:
The farmer wants the second side of the garden to be 30 feet longer than the back of his house.
If the back of his house=x ft
The second side=(x+30) ft
Note that the farmer does not fence the side on the back of the house.
Area of the garden = 400 square feet
Area of a Rectangle= Length X Width
400 = x(x+30)
[tex]x^2+30x-400=0\\x^2+40x-10x-400=0\\x(x+40)-10(x+40)=0\\(x+40)(x-10)=0\\[/tex]
x+40=0 or x-10=0
x=-40 or x=10
Since length cannot be negative, x=10 ft
The Length of the Fencing the farmer will buy will be the perimeter of the three sides.
Perimeter of the three sides = x+(x+30)+(x+30)
=3x+60
=3(10)+60=90 ft
The farmer needs to buy a fencing of length 90 feet.
The amount of fence the farmer will need to buy is; 90 ft
Now, let the length of the back of his house be x ft.
Thus, if the second side of the garden to be 30 feet longer than the back of his house, then the length of the second side is; (x + 30) ft.
Formula for area of a rectangle is;
Area = Length × width
Since the area of the garden is 400 ft², then we have;
400 = x * (x + 30)
400 = x² + 30x
x² + 30x - 400 = 0
Using quadratic equation solver online, we have;
x = -40 or 10
Since x cannot be negative, then we can say; x = 10 ft
Thus, length of second side = 10 + 30 = 40 ft
Since we are dealing with a rectangle, the second side will be parallel and equal to the third side. Then the perimeter will be;
Perimeter of 3 sides = 10 + 2(40)
Perimeter of 3 sides = 90 ft
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