Question

a square field has dimensions that are 3.3 times the corresponding dimensions of a similar square playground. which of the following statements is true? the area of the field is 3.3 times the area of the playground. the perimeter of the field is 3.3 times the perimeter of the playground. the perimeter of the field is 6.6 times the perimeter of the playground. the area of the field is 6.6 times the area of the playground.

Explanation:

Step1: Recall Similar Figures Properties

For similar figures, the ratio of perimeters is equal to the ratio of corresponding side lengths, and the ratio of areas is the square of the ratio of corresponding side lengths. Let the side length of the playground be \( s \), so the side length of the field is \( 3.3s \).

Step2: Analyze Perimeter Ratio

Perimeter of a square is \( 4 \times \text{side length} \). Perimeter of playground: \( P_p = 4s \). Perimeter of field: \( P_f = 4(3.3s)= 3.3\times(4s)= 3.3P_p \). So perimeter ratio is \( 3.3 \).

Step3: Analyze Area Ratio

Area of a square is \( \text{side length}^2 \). Area of playground: \( A_p = s^2 \). Area of field: \( A_f=(3.3s)^2 = 3.3^2s^2= 10.89A_p \), not \( 3.3 \) or \( 6.6 \) times.

Answer:

The perimeter of the field is 3.3 times the perimeter of the playground.