Notez cu x si y lungimile catetelor, iar cu h inaltimea.
[tex] \frac{x}{y}= \frac{4}{3}=>x=4k~si~y=3k. [/tex]
[tex] x^{2} + y^{2} = 80^{2} ~(T.~Pitagora)<=> \\ <=> (4x)^{2} +(3k)^{2}=6400<=> \\ <=> 16k^{2}+ 9k^{2} =6400<=> \\ <=>25 k^{2} =6400 => k^{2} =256=>k=16. \\ \\ x=4k=4*16=64 (cm)\\ y=3k=3*16=48(cm)[/tex]
[tex]h= \frac{x*y}{80}= \frac{64*48}{80}= 38,4(cm).[/tex]
