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.)
28.6 m^2
Correction from previous post. Similar triangles were not arranged correctly. (Thanks Jer.)
The area of the path is 11 m * EB. And as stated EB is not the width and thus is not 1 m.
Add new point G that lies on BF at a point that makes a perpendicular with point E.
EG = 1
Setting-up similar triangles:
BG / EG = (29 - EB) / AD
BG = (29-EB)/11
Also EG^2 + BG^2 = EB^2
EB^2 = BG^2 +1
Substituting: EB^2 = ((29-EB)/11)^2 +1
EB^2 = (841 - 58 EB + EB^2)/121 + 1
121 * EB^2 - 121 = 841 -58EB + EB^2
120EB^2 + 58 EB - 962 = 0
Real roots: EB = 2.6, (-3.083)
The area is then 11 m * 2.6 m = 28.6 m^2
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Posted by Leming
on 2006-05-10 14:47:17 |
Solution - guessing again
