Question

ABC triunghi oarecare
AB=5
AC=5√5
BC=10
Aria=?

Answer 1

p -semiperimetrul
p=(a+b+c)/2=(5+5√5+10)/2
formula lui Heron
A=√p(p-a)(p-b)(p-c)
dupa inlocuirea lui p, a, b, si c obtinem
A=√[(15+5√5)(15-5√5)(5√5+5)(5√5-5)]/16
aplicam sub radical formula a²-b²
A=√100·100/16=100/4=25
A=25

Answer 2

[tex]\it{A= \sqrt{p(p-a)(p-b)(p-c) }}\\\\ A= \sqrt{ \frac{(15+5 \sqrt{5} )(15-5 \sqrt{5} )(5 \sqrt{5} +5)(5 \sqrt{5} -5)}{16} }\\\\ A= \sqrt{ \frac{100*100}{16} } \\\\ A= \frac{100}{4} \\\\\bold{\it{A=25cm^2}}\\\\\\\\\\\\ p=semiperimetrul= \frac{a+b+c}{2} = \frac{5+5 \sqrt{5}+10 }{2}= \frac{15 +5\sqrt{5} }{2} [/tex]