Question

Square F has side lengths three times longer than the sides of square G. Which statement about their perimeter is true? O. A. The perimeter of square Fis one-half the perimeter of square G. B. The perimeter of square F is 2 times the perimeter of square G. C. The perimeter of square Fis one-third the perimeter of square G. D. The perimeter of square fis 3 times the perimeter of square G. O E. The perimeter of square fiis 9 times the perimeter of square G.

Answer 1

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:

`P_{\text{squareG}}=\text{ x+x+x+x= 4x}`

The perimeter of square F is:

`P_{\text{squareF}}=\text{ 3x+3x+3x+3x= 12x}`

The perimeter of square F (12x) is 3 times the perimeter of square G (4x)

This is because:

12x = 3 * (4x)

Thus:

`\begin{gathered} 12x=3*4x \\ P_(squareF)=3* P_{square\text{ G}} \end{gathered}`

Thus, from the options given, only option D is correct