Final answer:
To determine the perimeter of square 2 with twice the area of square 1 whose diagonal is a+b, we first find the side length of square 1, double it to get the side length of square 2, and then calculate the perimeter as four times the side length of square 2.
Step-by-step explanation:
First, we need to determine the side length of square 1. The diagonal of a square is a+b, so using the Pythagorean theorem for a square whose side is s, the diagonal is s√2. Thus, if the diagonal is a+b, the side length s is (a+b)/√2. To find the area of square 1, we square the side length, so area = ((a+b)/√2)².
Square 2 has twice the area of square 1. Therefore, if we let the area of square 1 be A, the area of square 2 is 2A. If s is the side length of square 1, then the side length of square 2, s2, must satisfy s2²=2A, which means s2=√(2)*s because the area of a square is the side length squared. Since the perimeter of a square is four times its side length, the perimeter of square 2 is 4√(2)*s.