Problema Solution
A garden has the shape of a right triangle with one leg 4 meterlonger than the other. The hypotenuse is 4 meters less than twice the length of the shorter leg. What is the length of the shorter leg?
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let
'a' and 'b' are the legs of the right triangle and a>b
'c' hypotenuse of the right triangle
one leg 4 meter longer than the other
a = b + 4
hypotenuse is 4 meters less than twice the length of the shorter leg
c = 2b - 4
using the Pythagorean Theorem we have
a^2 + b^2 = c^2
b^2 = c^2 - a^2
plug a = b + 4 and c = 2b - 4 into the last equation
b^2 = (2b - 4)^2 - (b + 4)^2
by solving the equation we find
b = 12 m
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the shorter leg is 12 meters long.