Question

Raportul ariilor a doua patrate este egal cu 36/25. Determinati raportul laturilor celor doua patrate si raportul perimetrelor celor doua patrate .

Daca x/2 = y/9 , atunci 10x-2y/5x+y =............

Daca 3x+4y/2x+y = 7/3 , atunci x/y= ?

Daca 6x+4y/5x+2y = 3/2 , atunci x/y =..

Daca 5x-4y/2x-y = 7/3 , 2x diferit y , atunci x/y =

Answer 1

A1/A2 = L1²/L2² = 36/25    (L1/L2)² = 36/25⇒  L1/L2 = 6/5    P1/P2 =4 L1/4L2= L1/L2=6/5

x/2 = y/9       y =9x/2= 4,5x ⇒    (10x-2y)/(5x+y) = (10x-9x)/ (5x+4,5x)  =                       x /9,5x =1/9,5=10/95=2/19

(3x+4y)/(2x+y) = 7/3       3(3x+4y) = 7 (2x+y)   ⇒9x +12y= 14x +7y ⇒ 5y = 5x ⇒ x = y ⇒ x/y =1/1

(6x +4y)/(5x+2y) =3/2    2(6x+4y) = 3(5x+2y)    12x + 8y = 15x +6y    2y = 3x  ⇒y =1,5x  x/y =x/1,5x = 1/1,5= 10/15 = 2/3  

(5x-4y)/(2x-y)=  7/3      3(5x-4y) = 7(2x-y)    15x-12y = 14x-7y⇒  x=5y⇒ x/y =5y/y =5/1