RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m.
How long are hypotenuse segments?

Correct result:

gb =  36 m
gt =  81 m

Solution:

gb+gt=117 gbgt=542  g2117g+2916=0  a=1;b=117;c=2916 D=b24ac=1172412916=2025 D>0  g1,2=b±D2a=117±20252 g1,2=117±452 g1,2=58.5±22.5 g1=81 g2=36   Factored form of the equation:  (g81)(g36)=0   gb=36 m
gt=81 m

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