Question

In triunghiul ABC stiu AB=8cm
BC=12cm
AC=6cm
Cum aflu distanta de la C la AB?

Answer 1

p = $\frac{AB+BC+AC}{2} = \frac{26}{2} =13 (cm)$ (p=semiperimetru)
$A_{ABC} = \sqrt{p(p-AB)(p-BC)(p-AC)}$ = $\sqrt{13*5*1*7} = \sqrt{455} (cm)$

$A_{ABC} = \frac{d(C;AB)*AB}{2} = \sqrt{455} cm.$ => d(A;BC)=$\frac{2* A_{ABC} }{AB} = [tex] \frac{2* \sqrt{455} }{8} = \frac{ \sqrt{455} }{4}$ (cm²)