Because, bisecting the base of the triangle gives of two segments of five. This forms two triangles with base of 5 and altitude (in this case height) of 12. There exists a special pythagorean triplet triangled named 5-12-13 meaning if you have a right triangle with two of these sides then the unknown side is the number left out. In this case, the altitude forms a right angle on the base which allows the sides of the big isocs. triangle to be 13 giving us 13 + 13 + 10 to be the perimeter = 36.
