Repuesta a = 9, b = 12
Teorema de Pitágoras
[tex] {h}^{2} = c {}^{2} + {c}^{2} [/tex]
[tex]15 {}^{2} = (x + 3) {}^{2} + (x) {}^{2} [/tex]
[tex]225 = 9 + 6x + {x}^{2} + {x}^{2} [/tex]
[tex]225 = 9 + 6x + 2 {x}^{2} [/tex]
[tex]0 = 2 {x}^{2} + 6x + 9 - 225[/tex]
[tex]0 = 2 {x}^{2} + 6x - 216[/tex]
[tex]0 = {x}^{2} + 3x - 108[/tex]
[tex]0 = (x + 12)(x - 9)[/tex]
Tomamos el valor positivo
[tex]x - 9 = 0[/tex]
[tex]x = 9[/tex]
Reemplazamos
[tex]cateto \: \: \: a = x = 9[/tex]
[tex]cateto \: \: \: b \: = x + 3 = 9 + 3 = 12[/tex]
