Question

which figure has a greater perimeter? 36.9 yd 36.9 yd 36.9 yd 36.9 yd 36.9 yd 59.3 yd 59.3 yd 66.4 yd

Explanation:

Step1: Calculate pentagon perimeter

The pentagon has 5 equal - side lengths of 36.9 yd. The perimeter formula for a regular pentagon is \(P = 5s\), where \(s\) is the side - length. So \(P_{pentagon}=5\times36.9 = 184.5\) yd.

Step2: Calculate triangle perimeter

The triangle has side - lengths 59.3 yd, 59.3 yd, and 66.4 yd. The perimeter formula for a triangle is \(P=a + b + c\). So \(P_{triangle}=59.3+59.3 + 66.4=185\) yd.

Step3: Compare perimeters

Compare \(P_{pentagon}=184.5\) yd and \(P_{triangle}=185\) yd. Since \(185>184.5\).

Answer:

The triangle has a greater perimeter.