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
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D F C
Find the exact area of the path.
(Note: EB is
not the width of the path.)
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
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Posted by Dej Mar
on 2006-05-10 17:25:18 |
Solution
