Răspunsuri

2014-09-02T09:27:22+03:00
A(0,a)B(-1,2)c(4,5)
Calculez lungimile laturilor aplicand formula:
AB =  \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} }      , , unde A(x1,y1) si B(x2,y2)

AB =  \sqrt{ (-1-0)^{2} + (2-a)^{2} }  =  \sqrt{ a^{2} -4a+5 }

BC =  \sqrt{ (4+1)^{2} +  (5-2)^{2} } = \sqrt{34}

AC =  \sqrt{ (4-0)^{2} +  (5-a)^{2} } =  \sqrt{ a^{2} -10a+41 }

Conditie ca triunghiul ABC sa fie dreptunghic:

 BC^{2} =  AB^{2} +  AC^{2}

34 = |  a^{2} -4a+5| + | a^{2} -10a+41|

34 =  2a^{2} -14a+46

 2a^{2} -14a+12 = 0     (impart ecuatia la 2)

a^{2} -7a+6=0

Δ = 49 - 24

Δ = 25

a1 = (7-5):2
a1=1

a2=(7+5):2
a2=12:2
a2=6

Raspuns final : a =1 sau a=6