Question

obwod prostokata ma 28cm, a jego przekatna ma dlugosc 2pierwiastki z 29cm. oblicz dlugosc bokow tego prostokata.

Answer 1

2a+2b = 28 |:2

a+b = 14

 

I bok - x

II bok - 14-x

 

x²+(14-x)² = (2√29)²

x²+(196-28x+x²) = (√116)²

x²+196-28x+x² = 116

2x²-28x = 116-196

2x²-28x = -80 |:2

x²-14x = -40

x²-14x+40 = 0

 

Δ = (-14)²-4*1*40

Δ = 196-160

Δ = 36

 

x₁ = [-(-14)-√36]/(2*1)

x₁ = (14-6)/2

x₁ = 8/2

x₁ = 4

x₂ = [-(-14)+√36]/2

x₂ = (14+6)/2

x₂ = 20/2

x₂ = 10

 

I bok - 4 lub 10

II bok - 10 lub 4