Question

Ex 1 va rog mult boiustef si albatran​

Answer 1

Răspuns:

Explicație pas cu pas:

PA⊥(ABC), PA=12cm, AB=16cm, AC=12cm, m(∡BAC)=90°.

a)d(P,B)=???  ΔPAB, dreptunghic in A, deci PB²=PA²+AB²=12²+16²=4²·3²+4²·4²=4²·(3²+4²)=4²·25, deci PB=√(4²·25)=4·5=20cm=d(P,B).

b) d(P,C)=???  ΔPAC, dreptunghic in A, deci PC²=PA²+AC²=12²+12²=12²·2, deci PC=√(12²·2)=12√2cm=d(P,C).

c) Aria(ΔPBC)=???  Vom Aplica formula lui Heron

p=(PB+BC+PC):2=20+20+12√2):2=10+10+6√2=20+6√2 (semiperimetrul)

Aria(ΔPBC)=√(p·(p-PB)·(p-BC)·(p-PC))=

=√((20+6√2)(20+6√2-20)(20+6√2-20)(20+6√2-12√2))=

=√((20+6√2)·6√2·6√2·(20-6√2))=√(20²-(6√2)²)·6²·2)=6·√((400-72)·2)=6·√(328·2)=6·√(4·82·2)=6·2·2√41=24√41cm²