Bunuel wrote:
A square garden is surrounded by a path of uniform width. If the path and the garden both have an area of x, then what is the width of the path in terms of x?
A. \(x \sqrt{2}\)
B. \(2 \sqrt{x} - \sqrt{2}\)
C. \(\frac{\sqrt{2}}{2} - \frac{x}{4}\)
D. \(x \sqrt{2} - \frac{x}{2}\)
E. \(\frac{\sqrt{2x}}{2} - \frac{\sqrt{x}}{2}\)
E is the answer
the area of the garden is 2x
side of the garden is square root of 2x
the shaded area is a trapezoid, its area equal 1/4 the area of the path, and its height is the width of the path.
you can see in the picture attached
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