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 ,
x2 + 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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