Question

A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 304 ft2. Find the width of the walkway if the garden is 12 ft wide by 15 ft long.

Answer 1

The width of the walkway around the community garden is 2 ft.

The given parameters;

• length of the garden = 15 ft

• width of the garden = 12 ft

• area of the garden and the walkway around its perimeter = 304 ft²

Let the width of the walkway = x

Length of the garden and the walkway = 15 + (x + x) = 15 + 2x

Width of the garden and the walkway = 12 + (x + x) = 12 + 2x

Area of the garden and the walkway = (15 + 2x)(12 + 2x)

304 = (15 + 2x)(12 + 2x)

304 = 180 + 30x + 24x + 4x²

304 = 180 + 54x + 4x²

divide through by 4;

76 = 45 + 13.5x + x²

x² + 13.5x  - 31 = 0

Solve the quadratic equation using formula method;

a = 1, b = 13.5, c = -31

$x = \frac{-b \ + /- \ \ \sqrt{b^2 -4ac} }{2a} \\\\x = \frac{-13.5 \ + /- \ \ \sqrt{(13.5)^2 -4(1\times -31)} }{2(1)} \\\\x = 2 \ \ \ or \ \ -15.5$

The width cannot be negative, so we choose 2 ft as the width of the walkway.

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