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.)
We also might have noticed that in sketching it out, ADE resembles a
5-12-13 triangle quite closely and tried multiplying all dimensions by
five to see where we were at. We know from similar triangles that EB is
1/11 of DE and when we checked to see that 29*5 was equal to 12*11 + 13
we'd know we were right!
The area of the path is equal to the length of DE which is the hypotenuse of a 5-12-13 triangle scaled up by 11/5.
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Posted by Eric
on 2006-05-11 20:24:55 |
A bit of a stretch
