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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 - guessing again | Comment 5 of 12 |

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


  Posted by Leming on 2006-05-10 14:47:17
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