Which one of the following has a greater perimeter than the rest ?

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Q: 143 (IAS/2000)
Which one of the following has a greater perimeter than the rest ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,9,4,4,0,9,0

keywords: 

{'greater perimeter': [0, 1, 0, 0], 'equilateral triangle': [0, 1, 0, 1], 'rectangle': [0, 1, 0, 1], 'sq cm': [0, 1, 0, 0], 'square': [0, 0, 0, 1], 'radius': [0, 0, 2, 2], 'circle': [0, 0, 2, 1], 'area': [0, 0, 0, 1], 'length': [0, 0, 1, 0]}

To determine which shape has the greater perimeter, we need to calculate the perimeter of each shape and compare them.

1. Square with an area of 36 sq cm:

The side length of the square can be calculated by taking the square root of the area. ?36 = 6 cm. The perimeter of a square is calculated by multiplying the side length by 4. Perimeter = 4 * 6 = 24 cm.

2. Equilateral triangle with a side of 9 cm:

The perimeter of an equilateral triangle is calculated by multiplying the side length by 3. Perimeter = 3 * 9 = 27 cm.

3. Rectangle with 10 cm as length and 40 sq cm as area:

To find the width of the rectangle, we divide the area by the length. Width = 40 cm² / 10 cm = 4 cm. The perimeter of a rectangle is calculated by adding the lengths of all sides. Perimeter = 2 * (length + width) = 2 * (10 cm + 4 cm) = 2 * 14 cm = 28 cm.

4. Circle with a radius of 4 cm:

The perimeter of a circle is called the circumference, and it is calculated using the formula 2?r, where r is the radius. Circumference = 2 * ? * 4 cm ? 25.13 cm.

Therefore, Rectangle with 10 cm as length and 40 sq cm as area, which aligns with option (c).