Question

# A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?

## The correct answer is: 13

### The length of garden in feet will be 13 feets.

For solving this question,

Let x represent the width of the rectangular garden, in feet.

Since we are given length of the garden will be 5 feet longer than the width of the garden,

The length of the garden will be x + 5 feet.

Thus the area of the garden will be

Area = (length)(width)

Area = x(x + 5).

It is also given that the area of the garden will be 104 square feet.

Therefore, x(x + 5) = 104,

Further solving we get ,

x^{2 }+ 5x −104 = 0.

The quadratic formula can be used or the equation above can be factorised as follows;

(w + 13)(w − 8) = 0.

Therefore, equating both the brackets with zero we get

w = 8 and w = −13

Because width cannot be negative, the width of the garden must be 8 feet.

This means the length of the garden will be

8 + 5 = 13 feet.

Therefore the length of the garden is 13 feets.

Note:- There are different ways of solving quadratic equations.

- Solving quadratic equations by factoring
- Solving quadratic equations by completing the square
- Solving quadratic equations by graphing
- Solving quadratic equations by quadratic formula

But most popular method is solving quadratic equations by factoring.

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