A garden has the shape of a right triangle with one leg 3 meters longer than the other. The hypotenuse is 3 meters less than twice the length of the shorter leg. What is the length of the shorter leg?

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Answer 1 · 2018-05-21T02:43:21

length is 9 meters.

let the unknown side be x so we have sides

x
x +3
2x-3

now we can use the Pythagorean theorem:

#a^2 + b^2 = c^2#

#x^2 + (x+3)^2 =(2x-3)^2#

#x^2 + x^2+6x +9 = 4x^2 -12x +9#

#2x^2+6x +9 -4x^2 + 12x -9 = 0#

#2x^2+6x -4x^2 + 12x = 0#

#-2x^2+18x = 0#

#-2x(x-9) = 0#

#x=9# we can ignore the 0 solution.

A garden has the shape of a right triangle with one leg 3 meters longer than the other. The hypotenuse is 3 meters less than twice the length of the shorter leg. What is the length of the shorter​ leg?