Question 567914
let the vertex be A where the legs meet

legs are 10 cm each
B & C are the vertices of the base

Law of Sines

a/sin A = b/sin B = c/sin C

a/sin 72 = 10/Sin 54 = c/Sin 54

a= 10*sin 72/Sin 54 
a= 11.75

So the perimeter = 11.75+10+10
perimeter = 31.75 cm