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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 7 of 12 |

The length of DE is given by Pythagorean's theorem as equal to the SQRT(AD2 + AE2).

The ratio of EB/1 = DE/AD, therefore EB = DE/11

By substitution:
112 + (29 - DE/11)2 = DE2

The polynomial can be equated to zero, thereby allowing the quadratic formula to be applied.

120/121DE2 +  58/11DE - 962 = 0  

As the solution must be a positive real number,
DE = 28.6 meters.

The area of the garden path is then 1 meter * 28.6 meters
= 28.6 sq. meters.

Edited on May 10, 2006, 9:18 pm
  Posted by Dej Mar on 2006-05-10 17:25:18

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