math
posted by Achillies on .
A garden has the shape of a right triangle with one leg 3 meters longer tha the other. The hypotenuse is 3 meters less than twice the lenght of the shorter leg.

b = a + 3
c = 2a 3
c^2 = a^2 + b^2 (Pythagorean theorem)
Solve those three equations simultaneously.
c^2 = 4a^2 12a +9
c^2 = a^2 + (a+3)^2 = 2a^2 +6a +9
2a^2 18a =0
a = 9
b = 12
c = 15 
s^2 + l^2 = h^2
s^2 + (s+3)^2 = (2s3)^2
s^2 + s^2 + 6 s + 9 = 4 s^2  12 s + 9
2 s^2  18 s = 0 = 2s(s9)
s = 0 or s = 9
the s = 0 root is irrelevant since that results in a negative hypotenuse
s = 9
l = 9+3 = 12
h = 15