Question

CONSIDERE AS MEDIDAS ABAIXO E CALCULE A HIPOTENUSA:
CATETO MEDE 6 E OUTRO CATETO MEDE 32
A)46,32
B)56,32
C)65,48
D)34,65
E)32,56
F)NDA

Answer 1

Teorema de pitágoras a soma dos catetos ao quadrado é igual a hipotenusa ao quadrado.

$\boxed{a^{2} = b^{2}+c^{2}}$

Onde a é a hipotenusa e b,c são os catetos

A) 46, 32

$a^{2} = b^{2}+c^{2}\\a^{2} = 46^{2}+32^{2}\\a^{2} = 2116+1024\\a^{2} = 3140\\a = \sqrt{3140}\\\boxed{a=56.0357029045}$

B) 56, 32

$a^{2} = b^{2}+c^{2}\\a^{2} = 56^{2}+32^{2}\\a^{2} = 3136+1024\\a^{2} = 4160\\a = \sqrt{4160}\\\boxed{a=64.4980619864}$

C) 65, 48

$a^{2} = b^{2}+c^{2}\\a^{2} = 65^{2}+48^{2}\\a^{2} = 4225+2304\\a^{2} = 6529\\a = \sqrt{6529}\\\boxed{a=80.8022276921}$

D) 34, 65

$a^{2} = b^{2}+c^{2}\\a^{2} = 34^{2}+65^{2}\\a^{2} = 1156+4225\\a^{2} = 5381\\a = \sqrt{5381}\\\boxed{a=73.3552997404}$

E) 32, 56

$a^{2} = b^{2}+c^{2}\\a^{2} = 32^{2}+56^{2}\\a^{2} = 1024+3136\\a^{2} = 4160\\a = \sqrt{4160}\\\boxed{a=64.4980619864}$

F) 6, 32

$a^{2} = b^{2}+c^{2}\\a^{2} = 6^{2}+32^{2}\\a^{2} = 36+1024\\a^{2} = 1060\\a = \sqrt{1060}\\\boxed{a=32.5576411922}$

Espero que seja isso!