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 Garden Path (Posted on 2006-05-10)
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)

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 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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