Fie lungimile catetelor - a și b
[tex]\dfrac{a}{b}=\dfrac{3}{4} \Rightarrow a=\dfrac{3b}{4}
\\
\sqrt{b^2+(\dfrac{3b}{4})^2}=40 \; (Pitagora) \\
\sqrt{b^2+\dfrac{9b^2}{16}}=40 \\
\sqrt{\dfrac{25b^2}{16}}=40\\
\dfrac{5b}{4}=40 \Rightarrow 5b=160 \Rightarrow b=32 \Rightarrow a=\dfrac{3\cdot32}{4}=24[/tex]
[tex]P_\Delta=32+24+40=96 cm[/tex]
