The perimeter of the two squares is 12 cm and 24 cm. The area of the bigger square is how many times that of the smaller?

The correct answer is: ∴ The Area of bigger square is 4 times that of the smaller square.

Step-by-step solution:-
Let Square 1 & Square 2 be the 2 squares
∴ For Square 1-
Perimeter 1 = 4 × side1
∴             12 = 4 side 1
∴        12 / 4 = side1
∴               3 = side1 ….......................... (Equation i)
Area 1 = (Side 1)²
∴ Area 1 = 3² ....................................... (From Equation i)
∴ Area 1 = 9 cm² .............................. (Equation ii)
∴ For Square 2-
Perimeter 2 = 4 × side2
∴             24 = 4 side 2
∴        24 / 4 = side 2
∴               6 = side2 ….......................... (Equation iii)
Area 2 = (Side 2)²
∴ Area 2 = 6² ....................................... (From Equation iii)
∴ Area 2 = 3⁶ cm² ................................ (Equation iv)
Ratio of Area of Bigger square to smaller square = Area of Bigger Square / Area of smaller square
∴ Ratio of Area of Bigger square to smaller square = Area of Square 2 / Area of smaller square 1
∴ Ratio of Area of Bigger square to smaller square = 36 / 9 ............................................................... (From Equations ii & iv)
∴ Ratio of Area of Bigger square to smaller square = 4