Hello,

the altitude divides the triangle into 2 right triangles. The legs of the isosceles triangle are the hypotenuses of the 2 right triangles and x is half of the base and it is one leg of a right triangle.

Now use Pythagorean theorem:

13² = 12² + x² ==> x² = 25 ==> x = 5

Therefore the base is 10 units long.