Question 745003
Let,
x - be the smaller leg
x+2 - (consecutive number)be the longer leg.

Area of triangle: {{{A=(x)(x+2)/2}}}
The numerical value of the area is three times that of the longer leg
{{{A = 3(x+2)}}}
Equate both area:
{{{(x)(x+2)/2=(x+2)}}}
{{{x^2-4x-12=0}}}
Use quadratic formula:
x = 6  smaller leg
x + 2 = 8 larger leg