Question

ALGUÉM ME AJUDA POR FAVOR É MUITO URGENTE ​

Answer 1

a)

$c=5\ cm;\ b=12\ cm;\ a=13\ cm;\ h=x\\\\ ah=bc\ \therefore\ 13x=12(5)\ \therefore\ \boxed{x=\dfrac{60}{13}\ cm}$

b)

$c=10\ cm;\ m=8\ cm;\ h=6\ cm;\ n=x\\\\ h^2=mn\ \therefore\ 6^2=8x\ \therefore\ \boxed{x=\dfrac{9}{2}\ cm}$

c)

$m=3\ cm;\ n=3\ cm;\ a=m+n=6\ cm;\ c=x\\\\ c^2=am\ \therefore\ x^2=6(3)\ \therefore\ x=\sqrt{3^2(2)}\ \therefore\ \boxed{x=3\sqrt{2}\ cm}$

d)

$m=3\ cm;\ h=4\ cm;\ b=x\\\\ h^2=mn\ \therefore\ 4^2=3n\ \therefore\ n=\dfrac{16}{3}\\\\ b^2=h^2+n^2\ \therefore\ x^2=4^2+\bigg(\dfrac{16}{3}\bigg)^2=16+\dfrac{16^2}{9}=\\\\ =\dfrac{9(16)+16(16)}{9}=\dfrac{16(25)}{9}\ \therefore\ x=\sqrt{\dfrac{16(25)}{9}}=\dfrac{4(5)}{3}\ \therefore\\\\ \boxed{x=\dfrac{20}{3}\ cm}$