Răspuns:
Explicație pas cu pas:
Δ ABC ; AH = 4 cm ; HC = 5 cm ; BH = ?
AC² = AH²+HC² = 4²+5² = 16+25 = 41 =>
AC = √41 cm
AC² = HC·BC => BC = AC²/HC = 41/5 =>
BH = BC-HC = 41/5 - 5 = (41-25)/5 = 16/5 = 3,2 cm
x = BH = 3,2 cm
Δ MNP ; MD = 6 cm (MD ⊥ PN) ; PD = 9 cm ; DN = ?
PM² = MD²+PD² = 6²+9² = 36+81 = 117
PM = √117 ; PM² = PD·PN => PN = PM²/PD = 117/9 = 13 cm
DN = PN - PD = 13-9 = 4 cm =>
y = DN = 4 cm
Δ DEF ; FH = 4 cm ; HE = 9 cm ; FE = 4+9 = 13 cm ; HD = ? HC = ?
(HC ⊥ DE)
FD² = FH·FE = 4·13 = 52 => FD = √52 = 2√13 cm
HD² = FD²-FH² = 52-16 = 36 => HD = 6 cm
DE² = HE·FE = 9·13 = 117 = > DE = 3√13 cm
Aria Δ DEH = DH·HE/2 = DE·HC/2 =>
HC = DH·HE/DE = 6·9/3√13 = 18/√13 = 18√13 /13 cm
t = HD = 6 cm ; z = HC = 18√13 /13 cm ≈ 5 cm
TRAPEZ GHIJ
GH = 25 cm ; KG = ? ; JG = ?
KG = GH = 25 cm
JK = GH = 25 cm =>
JG = 25√2 cm =>
u = KG = 25 cm
w= JG = 25√2 cm
#copaceibrainly
