Medians

Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.

Result

a =  6 cm
b =  20.78 cm
c =  21.63 cm

Solution:

 ta2=x2+(2y)2 tb2=y2+(2x)2  x2=ta24y2  y=4ta2tb215=10.39 x=ta24y2=3 a=2x=6  cm  \ \\ t_a^2 = x^2 + (2y)^2 \ \\ t_b^2 = y^2 + (2x)^2 \ \\ \ \\ x^2 = t_a^2-4y^2 \ \\ \ \\ y = \sqrt { \dfrac{ 4t_a^2-t_b^2 }{15} } = 10.39 \ \\ x = \sqrt { t_a^2 - 4y^2 } = 3 \ \\ a = 2x = 6 \ \text{ cm }
b=2y=20.78  cm b = 2y = 20.78 \ \text{ cm }
c=a2+b2=21.63  cm c = \sqrt{ a^2 + b^2} = 21.63 \ \text{ cm }

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