Question

In paralelogramul ABCD,m<A=60,AB=5,AD=4.Aflati a) distantele de la B la CD si la AD, b) lungimile diaginalelor paralelogramului.

Answer 1

a)
Aria ABCD = AB*AD*sinA= 5*4*$\sqrt{3}$/2=10$\sqrt{3}$
Aria= DC*d(B, CD)= 5*d(B, CD)=10$\sqrt{3}$
d(B, CD)=2$\sqrt{3}$

Aria= d(B, AD)*AD=10$\sqrt{3}$ => d(B, AD)*4=10$\sqrt{3}$
d(B, AD)=5$\sqrt{3}$/2

b) Construim BM perpendicular pe Da. Cum m<A=60 => m<ABM=30
Conform R. T. 30 => AM=2,5 => MD=1,5 => BM=5$\sqrt{3}$ /2
Aplicand teorema lui Pitagora in BMD => BD= $\sqrt{21}$

Fie AN perpendiucular pe BC (cade in exterior). Aplicand Teorema lui Pitagora in ANC => AC=$\sqrt{61}$