Find x if AB=x,BC=x+3, and AC=21?

AB+ BC = AC , so x + (x +3 )= 21 , 2x +3 = 21 , 2x = 18 , so x = 18/2 = 9 .

The angle ABC is required. If it is 90* then Pythagoras gives
x^2+(x+3)^2=21^2 giving
2x^2+6x-432=0 so
x^2+3x-216=0 and you can solve using a quadratic formula.

For other angles B, the Cosine Rule can be used giving
21^2=x^2+(x+3)^2-2x(x+3)cosB

Assuming a straight line
x + x + 3 = 21
2x = 18
x = 9

Suppose that BC is the hypotenuse of the right-angled triangle ABC.

BC² = AB² + AC² (Pythagoras' theorem)
(x + 3)² = x² + 21²
x² + 6x + 9 = x² + 441
6x = 432
x = 72

Is it a right-angled triangle ? or a line ABC ?

What is the relation between A, B & C?

AB + BC = AC → where: AB = x

x + BC = AC → where: BC = x + 3

x + x + 3 = AC → where: AC = 21

x + x + 3 = 21

2x + 3 = 21

2x = 18

x = 9