Triangle

Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.

Correct result:

a =  45
b =  28
c =  53

Solution:

S=ab2=a(a17)2=630  a217a1260=0  p=1;q=17;r=1260 D=q24pr=17241(1260)=5329 D>0  a1,2=q±D2p=17±53292 a1,2=17±732 a1,2=8.5±36.5 a1=45 a2=28   Factored form of the equation:  (a45)(a+28)=0  a=a1=45
b=a17=28
c=a2+b2=53

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