Question

which figure has a greater perimeter?
16.6 m 16.6 m 18.2 m 18.2 m
16.6 m 14.8 m
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Explanation:

Step1: Calculate perimeter of pink triangle

The pink triangle is equilateral with side \( 16.6 \, \text{m} \). Perimeter \( P_1 = 3 \times 16.6 \).
\( P_1 = 49.8 \, \text{m} \).

Step2: Calculate perimeter of blue triangle

The blue triangle has two sides \( 18.2 \, \text{m} \) and one side \( 14.8 \, \text{m} \). Perimeter \( P_2 = 18.2 + 18.2 + 14.8 \).
\( P_2 = 18.2 \times 2 + 14.8 = 36.4 + 14.8 = 51.2 \, \text{m} \).

Step3: Compare perimeters

Compare \( 49.8 \) and \( 51.2 \). Since \( 51.2 > 49.8 \), the blue triangle (second figure) has a greater perimeter.

Answer:

The blue triangle (the figure with sides \( 18.2 \, \text{m} \), \( 18.2 \, \text{m} \), and \( 14.8 \, \text{m} \)) has a greater perimeter.