Question

Considere as medidas da regiao triangular determinada pelo triangulo retangulo ao lado e determine : A) a,b,c e n B) a area da regiao triangular ABC

Answer 1

a) $6^{2}$=8.n
36=8n
n=$\frac{36}{8}$
n=4,5

$b^{2}$=$8^{2}$+$6^{2}$
$b^{2}$=64+36
$b^{2}$=100
b=√100
b=10

$c^{2}$=$6^{2}$+($\frac{45}{10}$)$^{2}$
$c^{2}$=36+$\frac{2025}{100}$
$c^{2}$=$\frac{5625}{100}$
c=√5625/100
c=$\frac{75}{10}$
c=7,5

$a^{2}$=$10^{2}$+($\frac{75}{10}$)$^{2}$
$a^{2}$=100+$\frac{5625}{100}$
$a^{2}$=$\frac{15625}{100}$
a=√15625/100
a=$\frac{125}{10}$
a=12,5

b)12,5. $\frac{6}{2}$
=$\frac{75} {2}$
=37,5 cm$^{2}$