Question 1118980
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The right angle is at C, so AB is the hypotenuse.  Then the Pythagorean Theorem says<br>
{{{(2x)^2+(x-5)^2 = (2x+1)^2}}}
{{{4x^2+x^2-10x+25 = 4x^2+4x+1}}}
{{{x^2-14x+24 = 0}}}
{{{(x-12)(x-2) = 0}}}<br>
x = 12  or  x = 2<br>
However, the solution x=2 gives a negative value for the length of one side of the triangle, so we choose the solution x=12.  Then the sides of the triangle are
2x=24; x-5=7; 2x+1 = 25<br>
The area of a right triangle is one-half the product of the lengths of the legs:
area = (1/2)(24)(7) = 84