Let us first represent the length of the sides of square G as x. The diagram below is a sketch of square G:
Now since the length of the sides of square F is three times longer than that of the length of the sides of square G, each side of square F will be equal to 3x. The diagram below is a sketch of square F:
Now, the perimeter of any plane shape is the sum of the lengths of all its sides.
Thus, the perimeter of square G is:
[tex]P_{\text{squareG}}=\text{ x+x+x+x= 4x}[/tex]
The perimeter of square F is:
[tex]P_{\text{squareF}}=\text{ 3x+3x+3x+3x= 12x}[/tex]
The perimeter of square F (12x) is 3 times the perimeter of square G (4x)
This is because:
12x = 3 * (4x)
Thus:
[tex]\begin{gathered} 12x=3\times4x \\ P_{squareF}=3\times P_{square\text{ G}} \end{gathered}[/tex]
Thus, from the options given, only option D is correct
