Use the distance formula in order to find the length of each side of the triangle.
>(7, 7) & (10, 3)
√[(7-10)² + (7-3)²] = 5
>(10, 3) & (7, 3)
√[(10-7)² + (3-3)²] = 3
>(7, 7) & (7, 3)
√[(7-7)² + (7-3)²] = 4
Adding all lengths (or solving for perimeter), we have: 5 + 3 + 4 = 12
The seamstress will need 12 inches of lace.