Răspuns :
1. construiesti inaltimea DM a paralelogramului
aflam DB in ΔADB, mB=90, AD=20, AB=25⇒Th Pitagora DB²= AB²-AD²
DB=√625-400=√225=15
A= DM*AB
A= 25*12=300
2.
a=5√5-√5=4√5
b=√(4√5-8)²= modul din 4√5-8
ma=(a+b)/2
ma=( 4√5+4√5-8)/2=(8√5-8)/2=4√5-4=4(√5-1)
ma=(4√5-4√5+8)/2=8/2=4
3.
p=(15+20+25)/2=60/2=30
A=√30(30-15)(30-20)(30-25)=√30*15*10*5=150
A=150
Am aplicat formula lui Heron
aflam DB in ΔADB, mB=90, AD=20, AB=25⇒Th Pitagora DB²= AB²-AD²
DB=√625-400=√225=15
A= DM*AB
A= 25*12=300
2.
a=5√5-√5=4√5
b=√(4√5-8)²= modul din 4√5-8
ma=(a+b)/2
ma=( 4√5+4√5-8)/2=(8√5-8)/2=4√5-4=4(√5-1)
ma=(4√5-4√5+8)/2=8/2=4
3.
p=(15+20+25)/2=60/2=30
A=√30(30-15)(30-20)(30-25)=√30*15*10*5=150
A=150
Am aplicat formula lui Heron
1) In Δdreptunghic ADB avem:
BD²=AB²-AD²=25²-20²=625-400=225=15²
BD=15
Aria Paralelogram= AD*BD=20*15=300 cm²
2) [tex] a=\sqrt{125} - \sqrt{5} [/tex]
[tex]b= \sqrt{ (4 \sqrt{5}-8 )^{2} } [/tex]
Media aritmetica =(a+b):2= (5√5-√5+4√5-8):2= (8√5-8):2= 4(√5-1)
3) se aplica Heron
A= [tex] \sqrt{p*(p-a)(p-b)(p-c)} [/tex]
p=(15+20+25):2=30
A=[tex] \sqrt{30*(30-15)(30-20)(30-25)} [/tex]
A=[tex] \sqrt{30*15*10*5} [/tex] = [tex] \sqrt{225000} [/tex] = 150
BD²=AB²-AD²=25²-20²=625-400=225=15²
BD=15
Aria Paralelogram= AD*BD=20*15=300 cm²
2) [tex] a=\sqrt{125} - \sqrt{5} [/tex]
[tex]b= \sqrt{ (4 \sqrt{5}-8 )^{2} } [/tex]
Media aritmetica =(a+b):2= (5√5-√5+4√5-8):2= (8√5-8):2= 4(√5-1)
3) se aplica Heron
A= [tex] \sqrt{p*(p-a)(p-b)(p-c)} [/tex]
p=(15+20+25):2=30
A=[tex] \sqrt{30*(30-15)(30-20)(30-25)} [/tex]
A=[tex] \sqrt{30*15*10*5} [/tex] = [tex] \sqrt{225000} [/tex] = 150