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# Quadratic equation Watch

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1. Hi, I have been stumped on this question but, feel like I may have the right answer. Any help would be greatly appreciated.

A new build estate requires a concrete path to be laid around the edge of each back garden. The first group of houses to be built have a garden 8m wide and 10m long. The path has constant width and is laid around the edge of the garden. If the area of the path is 100m2, calculate, by deriving a quadratic equation the width of the path (w) Find a quadratic expression to calculate the width of the path hence find the width using the known values. Create a spreadsheet to check your calculations and find an expression that could be used for gardens of different areas.

Working out:

8 x 10 = 80m^2
8+2x multiplied by 10+2x minus 80
(8+2x)(10+2x) - 80 = 100m^2
80 + 16x = 20x + 4x^2 - 80 = 100m^2
36x + 4x^2 = 100m^2

x^2 + 9x - 25 = 0

-b +/- √b^2 - 4ac
______
2a

-9 +/- √81-4(-25)
______
-50

-9 +/- √81+100
______
-50

-9 +/- √81-4x(x-25)

-9 +/- √181
______
2
x= -9 1
____ + ____ √181 = 2.22681202 metres for the width of the path
2. Anybody a friend of mine states that it is 2.4 (he rounded his answer up)
3. If the garden is 80 square metres, how can the area of the path be 100 square metres?
4. (Original post by mik1a)
If the garden is 80 square metres, how can the area of the path be 100 square metres?
Doesn't that mean only one house or garden can fit in the line of the path?
5. if the path is constant width it would need curved corners... it would not be rectangular in outline.
6. (Original post by the bear)
if the path is constant width it would need curved corners... it would not be rectangular in outline.
Hold on, doesn't it being constant width mean that the gardens or whatever are directly adjacent to each other?
7. (Original post by Kiritsugu)
Hold on, doesn't it being constant width mean that the gardens or whatever are directly adjacent to each other?
there is no way of knowing how the gardens are laid out in relation to one another.
8. I don't think this has anything to do with multiple gardens or the houses. It's about a rectangle within a rectangle, the dimensions of the outer rectangle are given and the difference in area between the rectangles are also given. However, the numbers provided in the question don't seem to make any sense.
9. lol I can't find anything on this - https://www.google.co.uk/search?q=%2...ck+garden.+%22

Where did you find this question?
10. Hold on, if one garden is 8m, then how can the path be 2.22681202 metres in width?
11. What am I doing with my life...
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Updated: October 8, 2016
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