Question

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the length of a rectangular garden is 10 feet longer than its width. if the gardens perimeter is 188 feet, what is the area of the garden in square feet?

Explanation:

Step1: Define variables

Let the width of the garden be \( w \) feet. Then the length \( l = w + 10 \) feet.

Step2: Use perimeter formula

The perimeter of a rectangle is \( P = 2(l + w) \). We know \( P = 188 \), so:

$$ 188 = 2((w + 10) + w) $$

Step3: Solve for width

Simplify the equation:

$$ 188 = 2(2w + 10) \\ 188 = 4w + 20 \\ 4w = 188 - 20 \\ 4w = 168 \\ w = \frac{168}{4} \\ w = 42 $$

Step4: Find length

Length \( l = 42 + 10 = 52 \) feet.

Step5: Calculate area

Area of a rectangle is \( A = l \times w \), so:

$$ A = 52 \times 42 = 2184 $$

Answer:

2184