Question

by how much would the perimeter of the square bi increased if the area is tripled.

Answer 1

I experimented: first, I let A = 1, which would imply that the length of each side of the square is 1; thus, the perimeter is 4. Next, I let A = 3 (triple the old area), which would imply that the length of each side is Sqrt(3); thus, the perimeter would be 4*Sqrt(3). In summary, it appears that if the area of the square is tripled, the perimeter increases by a factor of Sqrt(3). kc_kennylau has provided a more general and more sophisticated solution; the only change I'd make in his drawing would be to type Sqrt(3) in place of root(3).