Is it true that the sum of squares of perpendicular medians in a triangle is equal to the square of the third median?

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I am aware of the fact that two medians are perpendicular in a triangle if and only if the

Sum of the squares of the lengths of the sides to which these medians are drawn is $5$ times greater than the squared length of the third side.

However, I was also able to get the result that

Sum of squares of perpendicular medians $=$ Square of the third median

Can someone please confirm if my result is true or not as I was not able to get any answer from looking up on the web? Please help!!!

Thanks in advance !!!