Răspuns:
Explicație pas cu pas:
a) BC²=AB²+AC²
BC²=12²+16²=144+256=400
BC=20cm
In ΔABD dreptunghic avem:
AB²=AD²+BD²
144=AD²+BD²
In ΔACD dreptunghic avem:
AC²=AD²+CD²
256=AD²+CD²
scazand cele doua ecuatii avem:
256-144=CD²-BD²
112=CD²-(BC-CD)²
112=CD²-400+2BC×CD-CD²
400+112=40CD
512=40CD
CD=12,8cm
BD=BC-CD
BD=20-12,8=7,2cm
AD²=256-CD²
AD²=256-163,84=92,16cm
AD=√92,16=√(4²×2²×1,2²)
AD=4×2×1,2=9,6cm
b) Similar obtinem:
BD²=15²-12²=225-144=81
BD=9cm
AC²=12²+CD²
AC²=144+CD²
AC²=BC²-15²
AC²=(CD+9)²-225
CD²+81+18CD-225=144+CD²
18CD=288
CD=16cm
BC=16+9=25cm
c) AC²=30²-18²=900-324=5756
AC=16cm
Similar a), obtinem:
18²=AD²+BD²
26²=AD²+CD²
576-324=CD²-(30-CD)²
252=-900+60CD
CD=19,2cm
BD=30-19,2=10,8cm
AD²=576-19,2²
AD²=386,64
AD=8√0,41cm
d) BC=12+27=39cm
AB²+AC²=39²
AD²+12²=AB²
AD²+27²=AC²
Adunand ultimele doua ecuatii, obtinem;
2AD²+144+729=39²
2AD²=648
AD²=324
AD=18cm
AB²=AD²+12²
AB²=468
AB=6√13cm
AC²=AD²+27²
AC²=9√13cm
