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Garden Path (Posted on 2006-05-10) Difficulty: 3 of 5
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.)

See The Solution Submitted by Jer    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 6 of 11 |
 
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 2006-05-10 15:00:31
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