A gardener has a rectangular garden 11m (AD) by 29m (AB) and wants to install a diagonal path exactly 1m wide. The edges of the path are ED and BF as shown in the diagram.
A_____________E__B
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|/__/____________|
D F C
Find the exact area of the path.
(Note: EB is not the width of the path.)
Call the length DF as x. We then have
11*29 - 11*(29-x) = sqrt(11^2 + (29-x)^2)
Which simplifies to the quadratic
120x^2 +58x - 962 = 0
and has the positive solution x=2.6
So the area of the path = 2.6*11 = 28.6 m^2
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