Question

Un dreptunghi ABCD are AB=8cm BC=4.cat masoara distanta de la pct. A pana la diag. BD?

Answer 1

Calculam cu Teorema lui Pitagora diagonala dreptunghiului
BD²=AB²+AD² ⇒BD²=64+16 ⇒BD²=80 ⇒BD=4√5 cm
si apoi calculam distanta d(A,BD), adica perpendiculara dusa din A pe BD
d(A,BD)=h in Δ BAD , iar h=c₁×c₂/ip ⇒h=AB×AD/BD ⇒
h=8×4/4√5 ⇒h=8√5/5 cm
h=$\frac{8 \sqrt{5} }{5}$

Answer 2

BD²= AB² + AD² = 64 +16 =80
BD=√80 = √2⁴ · 5 = 2²√5= 4√5
Calculam aria ΔABD(dreptunghic) in doua moduri 
SΔABD=(C·C)/2= AB·AD/2
SΔABD =( i·h)/2= BD·i /2
⇒ AB·AD= BD·i 
i= (AB·AD)/BD= 8·4/4√5= 8/√5= 8√5/5