Question

Se alguém souber, me ajudem pfvvvv

Answer 1

Resposta:

Alternativa D

Explicação passo-a-passo:

Vamos utilizar apenas Teorema de Pitágoras:

$hip^{2} =cat^{2} +cat^{2} \\a^{2} =b^{2} +c^{2} \\a^{2} =6^{2} +8^{2} \\a=\sqrt{100} \\a=10$

$a =m+n\\m=a-n\\m=10-n$

$b^{2} =h^{2} +m^{2} \\6^{2} =h^{2} +(10-n)^{2} \\36=h^{2} +10^{2}-20n+n^{2} \\h^{2} =36-100+20n-n^{2} \\h=\sqrt{-64+20n-n^{2} }$

$hip^{2} =cat^{2} +cat^{2} \\c^{2} =n^{2} +h^{2} \\8^{2} =n^{2} +(\sqrt{-64+20n-n^{2} } )^{2} \\64=n^{2}-64+20n-n^{2} \\64+64=20n\\n=\frac{128}{20} \\n=6,4$

$h=\sqrt{-64+20n-n^{2} } \\h=\sqrt{-64+20(6,4)-6,4^{2} } \\h=\sqrt{23,04} \\h=4,8$