**Question:**A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?

**Answers:**

width of path = x

(20-2x)(30-2x) = 400

600 - 40x - 60x + 4x^2 = 400

4x^2 -100x + 200 = 0

4(x^2 - 25x + 50) = 0

x^2 - 25x + 50 = 0

x = [25 +- sqrt(625 - 200) ] / 2

x = [25 +- sqrt(425) ] / 2

x = (25 +- 20.62)/2

x = 2.19 (22.81 is not feasible)

width of path is approximately 2.2 ft

which means the garden is approximately 15.6 ft by 25.6 ft

What is ^2?

I find no such symbol for a mathematical calculation

area of the garden(before the path installed): 30x20=600 ft^2

area of remaining garden area: 400 ft^2

Thus, area of the path is: 600-400=200 ft^2

the length of the path will be 20+20+30+30=100 ft

Thus the width of the path will be 200/100=2 ft.

The width of the path is 2 ft

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