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

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