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.)
11.823 m^2
The area of the path is 11 * EB. And as stated EB is not the width and thus is not 1m.
Setting-up similar triangles:
Add new point G that lies on BF at a point that makes a perpendicular with point E.
EG = 1
BG / EG = AD / (29 - EB)
Substituting: BG = 11/(29-EB)
Also EG^2 + BG^2 = EB^2
or EB^2 = BG^2 +1
I used Excel's equation solver I got EB = 1.075 m (1.074785)
The area is then 11 m * 1.075 m = 11.823 m^2
Edited on May 10, 2006, 12:37 pm
|
|
Posted by Leming
on 2006-05-10 12:35:42 |
Solution- I guess
