Question

which figure has a greater perimeter? 62 m 62 m 62 m 75 m 45 m 60 m

Explanation:

Step1: Calculate the perimeter of the first triangle

The first triangle is equilateral with side \(a = 62\) m. The formula for the perimeter of a triangle is \(P=\sum_{i = 1}^{3}a_{i}\). For an equilateral triangle \(P = 3a\).

$$P_1=3\times62= 186\space m$$

Step2: Calculate the perimeter of the second triangle

The second triangle has sides \(a = 75\) m, \(b = 45\) m, \(c=60\) m. Using the perimeter formula \(P=\sum_{i = 1}^{3}a_{i}\)

$$P_2=75 + 45+60=180\space m$$

Step3: Compare the perimeters

Since \(186>180\), the first figure has a greater perimeter.

Answer:

The first figure (equilateral triangle) has a perimeter of \(186\) m. The second figure (right - angled triangle) has a perimeter of \(180\) m. So, the first figure has a greater perimeter.