catete b si c
ipotenuza a
aria = bc/2 =1320
bc= 2640
a² = b² + c² ; 73² = b² + c²
dar b² + c² = b² +c² + 2bc - 2bc = ( b² +c² +2bc) -2bc = ( b +c)² - 2bc =
= ( b +c)² - 2 ·2640 = ( b +c)² - 5280
5329= ( b +c)² - 5280
5329 + 5280 = ( b +c)²
10609 = ( b +c)²
√10609 = √( b+c)² ⇒ b +c = 103
suma nec = b +c = 103
prod. nec = bc = 2640
formam ec. de gr.II : x² -103x + 2640 = 0 ; Δ=10609 - 10560
Δ = 49 ; √Δ = 7
x₁=( 103 - 7) /2 = 48
x₂ = ( 103 +7) /2 = 55
radacinile sunt catelele : b = 48 cm ; c = 55 cm
