Question 74456
the three sides are x +(x+1)+(x+2)
x^2+(x+1)^2=(x+2)^2
x^2+x^2+2x+1=x^2+4x+4
2x^2-x^2-2x-4x+1-4=0
x^2-6x-3=0 using the quadratic equation we get:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} this is the quadratic equation.
x=(6+-sqrt[36-4*1*-3])/2*1
x=(6+-sqrt[36+12])/2
x=(6+-sqrt48)/2
x=(6+-6.928)/2
x=(6+6.928)/2
x=12.928/2
x=6.464 is the length of the smallest side.
x+1=7.464 is the next longest side.
x+2=8.464 is the hypotenuse of this triangle.