Bunuel wrote:
The figure above shows a rectangular garden that is comprised of a central plot and a border surrounding the central plot; the border and the central plot have the same area. The garden has length 25 feet and width 20 feet. If the length and width of the central plot have the same ratio as the length and width of the garden, what is the length of the central plot, in feet?
A. \(25\sqrt{2}\)
B. \(20\sqrt{2}\)
C. \(20(1-\sqrt{2})\)
D. \(\frac{25\sqrt{2}}{2}\)
E. (25/2)^2
General equationArea of center = LW
Area of border = area of center = LW
Center + border = Total area (25*20)
\(2(LW) = 500\)
\(LW = 250\)
Use the ratio to eliminate WThe ratio of length to width of total area (garden) = ratio of length to width for center
\(\frac{L}{W} = \frac{25}{20} = \frac{5}{4}: 5W = 4L --> W = \frac{4}{5}L\)
Substitute and solve for length\(LW = 250\)
\(W = \frac{4}{5}L\)
\(\frac{4}{5}L*L = 250\)
\(\frac{4}{5}L^2 = 250\)
\(L^2 =
250 * \frac{5}{4}\)
**\(L^2 =\frac{25*10*5}{4} = \frac{(25)*2*(5)*(5)}{4}\)
\(L =\frac{25\sqrt{2}}{2}\)
Answer D
**OR
\(L^2 = (250 *\frac{5}{4}) =(\frac{1250}{4}) =(\frac{2*5*5*5*5}{4})\)
\(L =\frac{25\sqrt{2}}{2}\)
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