Question

determine x e y nas figuras:

Answer 1

a)
$y=m+n\\\\ m^2+1^2=(\sqrt{5})^2\\ m^2+1=5\\ m^2=4\\ m=\pm \ 2\\ m=2\\\\ y=2+n\\ n=y-2\\\\ n^2+1^2=x^2\\ n^2+1=x^2\\ (y-2)^2+1=x^2\\ y^2-4y+4+1=x^2\\ y^2-4y+5=x^2\\\\ y^2=(\sqrt{5})^2 + x^2\\ y^2=5+x^2\\\\ y^2-4y+5=x^2\\ 5+x^2-4y+5=x^2\\ -4y=-10\\\\ y=\frac{-10}{-4}\\\\ y=\frac{5}{2}\\\\ y^2=5+x^2\\\\ (\frac{5}{2})^2=5+x^2\\\\ \frac{25}{4}=5+x^2\\\\ x^2=\frac{25}{4}-5\\\\ x^2=\frac{5}{4}\\\\ x=\frac{\sqrt{5}}{2}$

b)

$h^2+2^2=3^2\\ h^2+4=9\\ h^2=5\\ h=\sqrt{5}\\\\ h^2+x^2=y^2\\ (\sqrt{5})^2+x^2=y^2\\ 5+x^2=y^2\\\\ 3^2+y^2=(x+2)^2\\ 9+y^2=x^2+4x+4\\ 9+5+x^2=x^2+4x+4\\ 4x=9+5-4\\ 4x=10\\ x=\frac{5}{2}\\\\ y^2=x^2+5\\ y^2=(\frac{5}{2})^2+5\\\\ y^2=\frac{25}{4}+5\\\\ y^2=\frac{25+20}{4}\\\\ y^2=\frac{45}{4}\\\\ y=\sqrt{\frac{45}{4}}\\\\ y=\frac{3\sqrt{5}}{2}$