Question

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?

• A. 5 m
• B. 8 m
• C. 7 m
• D. 11 m

Hint:

In a rectangle, use the area formula \(A = \text{length} \times \text{width}\) to set up an equation and solve for unknown dimensions.

Answer 1

The Correct Option is B

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.