Question

Aria unui triunghi dreptunghic cu ipotenuza de 16 cm este de 32(radical)3 cm. (patrati) . Determinati lungimile catetelor

Answer 1

[tex]A= \frac{c_1\cdot c_2}{2} =32\sqrt{3}=\ \textgreater \ c_1\cdot c_2=64\sqrt{3}\\ c_1^2+c_2^2=16^2=256\\ (c_1+c_2)^2-2c_1c_2=256\\ (c_1+c_2)^2=256+2\cdot64\sqrt{3}\\ (c_1+c_2)^2=256+128\sqrt{3}\\ c_1+c_2= \sqrt{256+128\sqrt{3}} =8\sqrt{3}+8\\ c_1=8\sqrt{3}\\ c_2=8[/tex]