DEF is a right triangle; DE = 12, EF = x – 1, DF = x + 1.

Answer 1

Let 12 be the hypotenuse

then

144 = x^2 +2x + 1 + x^2 -2x +1 = 2x^2 +2

x^2 = 71

x =sqr71 = about 8.4

then x+1 = 9.4 and x-1 = 7.4

it could be a 12-9,4-7.4 right triangle

That might be the solution, but try x+1 as the hypotenuse. x-1 is definitely less than x+1 so x-1 can't be the longest side

x^2 + 2x + 1 = 144+ x^2 -2x + 1

4x = 144

x = 36

x+1 = 37, x-1 = 35.

then

it's a 37-35-12 right triangle.

two possible solutions. That came out so even, that maybe that's what the problem was designed for.

37^2 = 35^2 + 12^2

1369 = 1225 + 144