A farmer plans to build a rectangular garden in back of his house so that he only needs fencing on 3 sides of the garden. if he wants the second side of the garden to be 30 feet longer than the back of his house, and the area of the garden is going to be equal to 400 square feet, how much fence does he need to buy?

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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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)

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.