Question

Fie triunghiul dreptunghic ABC cu unghiul A=90 grade. Petrimetrul triunghiului este 72 cm si AB/3=AC/4. Calculati ipotenuza

Answer 1

$\left \{ {{ \frac{AB}{3} = \frac{AC}{4} } \atop {AB+BC+AC=72}} \right. \ \textless \ =\ \textgreater \ \left \{ {{AB= \frac{3AC}{4} } \atop {BC+\frac{3AC}{4} +AC=72}} \right. \ \textless \ =\ \textgreater \ BC=72- \frac{7AC}{4}$
BC²=AB²+AC²
BC²=$\frac{9}{16}$AC²+AC²
BC²=$\frac{25}{16}$AC²=$\frac{5}{4}$AC
Egalam partile
$\frac{5}{4}$AC=72-$\frac{7}{4}$AC
3AC=72
AC=24 cm
BC=$\frac{5}{4}$*24=30 cm