Question

Pole trójkąta prostokątnego wynosi 180 cm kwadratowych, a przeciw prostokątna 41 cm.Oblicz obwód tego trójkąta.

Answer 1

P= 180 cm²

c = 41 cm

c² = a² + b²

41² = a² + b²

1681 = a² + b²

a² = 1681 - b²

a =√(1681-b²)

P = ½ a*b

180 = ½ √(1681-b²) * b    /*2

360 = √(1681-b²) *b    I²

129600 = (1681-b²) *b²

- b⁴ + 1681b² -129600 = 0 

b² = t

-t² + 1681t – 129600 = 0

∆ = b² - 4ac

∆ = 1681² - 4*129600 = 2825761 – 518400 = 2307361

√∆ = √2307361 = 1519

x₁ = (  -b-√∆)/2a  = (-1681 -1519)/-2 = -3200/-2 = 1600

x₂ = (  -b+√∆)/2a  = (-1681+1519)/-2 = -162/-2 = 81

b₁² = 1600

b ₁= √1600

b ₁= 40 cm

 

b₂² = 81

b₂ =√81

b₂ = 9  cm

 

a₁=√(1681-b²)

a₁ = √(1681-40²) = √(1681-1600) = √81

a₁ = 9 cm

 

a₂=√(1681-b²)

a₂ = √(1681-9²) = √(1681-81) = √1600

a₂ = 40

 

a₁ = 9 cm

b₁ = 40  cm

 

a₂ = 40 cm

b₂ = 9 cm

 Obw = a+b+c

Obw = 9 + 40 + 41 = 90 cm