# 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.

Correct result:

a =  6 cm
b =  20.78 cm
c =  21.63 cm

#### Solution:

$\ \\ t_a^2 = x^2 + (2y)^2 \ \\ t_b^2 = y^2 + (2x)^2 \ \\ \ \\ x^2 = t_a^2-4y^2 \ \\ \ \\ y = \sqrt { \dfrac{ 4t_a^2-t_b^2 }{15} } = 10.39 \ \\ x = \sqrt { t_a^2 - 4y^2 } = 3 \ \\ a = 2x = 6 \ \text{cm}$
$b = 2y = 20.78 \ \text{cm}$
$c = \sqrt{ a^2 + b^2} = 21.63 \ \text{cm}$

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