Answers To Your Questions About A Square Garden Plot Measures
Carol asks…
A rectangular plot of ground measures 10 meters by 6 meters. A path is to be constructed within the plot so th?
**A rectangular plot of ground measures 10 meters by 6 meters. A path is to be constructed within the plot so that a 12 square meters garden can be planted with the path surrounding it. If x is the width of the path, find the width of the path
Green Thumb answers:
Let the overall length, L = 10, the overall width, W = 6, and the width of the path be “x”. The dimensions of the garden, therefore, are:
l = L – 2x
w = W – 2x
And the area of the garden is:
A = lw = (L – 2x)(W – 2x) = 12
Since L = 10 and W = 6:
(10 – 2x)(6 – 2x) = 12
2(5 – x)2(3 – x) = 12
(5 – x)(3 – x) = 3
15 – 5x – 3x + x² = 3
Rearranging:
x² – 8x + 12 = 0
(x – 2)(x – 6) = 0
The path width is x = 2 or x = 6 meters:
Check x = 2:
A = lw = [10 - 2(2)][6 - 2(2)] = (6)(2) = 12 m²
Check x = 6:
A = lw = [10 - 2(6)][6 - 2(6)] = (-2)(-6) = 12 m²
Since the length and width cannot be negative, the only solution is x = 2.
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