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
 / /
 / / 
 / / 
 / / 
 / / 
 / / 
/__/____________
D F C
Find the exact area of the path.
(Note: EB is
not the width of the path.)
From the figure we have the following equations:
(DE)^2 = (AD)^2 + (AE)^2
AE = AB  EB
EB DE
 = 
1 AD
Removing AE and EB gives the following quadratic:
[(AD)^2  1](DE)^2 + [2(AB)(AD)](DE)  [(AB)^2 + (AD)^2](AD)^2 = 0
Substituting AB = 29 and AD = 11 gives:
120(DE)^2 + 638(DE)  116402 = 0
Solving for the positive root gives:
DE = 28.6
The area of the path is (DE)(1) = 28.6 m^2.

Posted by Bractals
on 20060510 15:00:31 