A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 88 square meters, what is the width of the garden?
Show Hint
- 5 m
- 8 m
- 7 m
- 11 m
The Correct Option is B
Solution and Explanation
To solve for the width of the rectangular garden, we need to set up an equation using the information given. Let's define the width of the garden as \( w \) meters. According to the problem, the length of the garden is 3 meters more than the width, so it can be written as \( w + 3 \) meters.
The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the garden is:
\( \text{Area} = \text{Length} \times \text{Width} = (w + 3) \times w = 88 \)
This equation can be expanded and rearranged as follows:
\( w^2 + 3w = 88 \)
Subtract 88 from both sides to set the equation to zero:
\( w^2 + 3w - 88 = 0 \)
This is a quadratic equation in the form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = 3 \), and \( c = -88 \). To find the value of \( w \), we can use the quadratic formula:
\( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
Plug in the values of \( a \), \( b \), and \( c \):
\( w = \frac{-3 \pm \sqrt{3^2 - 4 \cdot 1 \cdot (-88)}}{2 \cdot 1} \)
\( w = \frac{-3 \pm \sqrt{9 + 352}}{2} \)
\( w = \frac{-3 \pm \sqrt{361}}{2} \)
The square root of 361 is 19, so:
\( w = \frac{-3 \pm 19}{2} \)
This gives us two potential solutions for \( w \):
- \( w = \frac{16}{2} = 8 \)
- \( w = \frac{-22}{2} = -11 \)
Since the width of the garden cannot be negative, the width must be \( w = 8 \) meters.
Therefore, the width of the garden is 8 meters, which is the correct answer.
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