A square garden is surrounded by a path of uniform width. If the path

Question

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}

Luckisnoexcuse · Answer

consider x as 4 then side of square will be 2
now side of square +path =  2\sqrt{2} 
width =  (2\sqrt{2} - 2)/2  =  \sqrt{2}-1 
substituting 4 in place of x in options
E

abhinashgc · Answer

How now side of square +path =  2\sqrt{2} ???

Thanks

jess1231 · Answer

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

JeffTargetTestPrep · Answer

\

Since the square garden has an area of x, its side length is √x. Since the square garden is surrounded by a path of uniform width, the shape of the path and garden combined is also a square. We can let the width of the path = n, and thus the side length of the square that is the path and garden combined is √x + 2n. Since the total area of the path and garden is x + x = 2x, we have:

(√x + 2n)^2 = 2x

Taking the square root of both sides, we have:

√x + 2n = √(2x)

2n = √(2x) - √x

n = √(2x)/2 - √x/2

Answer: E

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A square garden is surrounded by a path of uniform width. If the path

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A square garden is surrounded by a path of uniform width. If the path

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