[tex] Fie \ a \ cateta \ 1, \ b - cateta \ 2, \ c - ipotenuza, \ c_1 - proectia \\ catetei \ 1 \ pe \ ipotenuza, \ iar \ c_2 - proectia \ catetei \ 2 \ pe \ ipotenuza; \\ a=b=6\sqrt2 \\ a^2=c \cdot c_1 \\ b^2=c \cdot c_2 \\ c^2=a^2+b^2 \\ c=\sqrt{a^2+b^2}= \sqrt{(6\sqrt2)^2+(6\sqrt2)^2} = \sqrt{2(6^2+\sqrt2^2} ) \\ c= \sqrt{2(36 +2)} = \sqrt{2 \cdot 38} = \sqrt{76} =2 \sqrt{19} \\ c_1= \frac{a^2}{c} = \frac{(6\sqrt2)^2}{2\sqrt{19}} = \frac{36 \cdot 2}{2\sqrt{19}} = \frac{72}{2\sqrt{19}} =\frac{36}{\sqrt{19} [/tex]
[tex]c_2= \frac{b^2}{c} = \frac{(6\sqrt2)^2}{2\sqrt{19}} = \frac{6^2 \cdot \sqrt2^2}{2\sqrt{19}} = \frac{36 \cdot 2}{2 \sqrt{19}} =\boxed{ \frac{36}{\sqrt{19}} } \\ \Rightarrow \boxed{c_1=c_2= \frac{36}{\sqrt{19}} }[/tex]
