# Medians in right triangle

It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?

Result

a =  11.685 cm
b =  5.465 cm
c =  12.9 cm

#### Solution:

$t_{ 1 } = 8 \ cm \ \\ t_{ 2 } = 12 \ cm \ \\ \ \\ t_{ 1 }^2 = x^2 + (2y)^2 \ \\ t_{ 2 }^2 = y^2 + (2x)^2 \ \\ \ \\ x^2 = t_{ 1 }^2-4y^2 \ \\ \ \\ y = \sqrt{ \dfrac{ 4 \cdot \ t_{ 1 }^2-t_{ 2 }^2 }{ 15 } } = \sqrt{ \dfrac{ 4 \cdot \ 8^2-12^2 }{ 15 } } \doteq 2.7325 \ cm \ \\ x = \sqrt{ t_{ 1 }^2 - 4 \cdot \ y^2 } = \sqrt{ 8^2 - 4 \cdot \ 2.7325^2 } \doteq 5.8424 \ cm \ \\ \ \\ a = 2 \cdot \ x = 2 \cdot \ 5.8424 \doteq 11.6847 = 11.685 \ \text { cm }$
$b = 2 \cdot \ y = 2 \cdot \ 2.7325 \doteq 5.465 = 5.465 \ \text { cm }$
$a^2+b^2 = c^2 \ \\ \ \\ c = \sqrt{ a^2 + b^2 } = \sqrt{ 11.6847^2 + 5.465^2 } \doteq 12.8998 = 12.9 \ \text { cm }$

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Looking for help with calculating roots of a quadratic equation? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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