Question 140230
4^2=x^2+(x+1)^2
16=x^2+x^2+2x+1
2x^2+2x+1-16=0
2x^2+2x-15=0
Using the quadratic equation:{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a)}}}we get:
x=(-2+-sqrt[-2^2-4*2*-15])/2*2
x=(-2+-sqrt[4+120])/4
x=(-2+-sqrt124)/4
x=(-2+-11.1355)/4
x=(-2+11.1355)/4
x=9.1355)/4
x=2.28 for the shorter leg.
2.28+1=3.28 for the longer leg.
proof
16=2.28^2+3.28^2
16=5.2+10.8
16=16