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Is it true that the wire bent in the form of a square of side 10cm encloses more area than a rectangle which is 12cm long?

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True

False

answer is A.

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Detailed Solution

To find if the square shape bent wire encloses more area or not, first, we need to find the area of the square.
Area of square

= s i d e 2

= 10 c m 2

= 100 c m 2

Also, we know that both squares and circles are made from the same length of wire so they will have the same perimeter.
The perimeter of a square is equal to

4 × s i d e

and perimeter of a rectangle that is

2 (l + b)

, where l is the length and b is the breadth.

4 × s i d e = 2 (l + b)

4 × 10 = 2 (12 + b)

b = 20 c m − 12 c m

b = 8 c m

Now, we can find the area of the rectangle using the formula

l e n g t h × b r e a d t h

l × b = 12 c m × 8 c m

= 96 c m 2

Thus, the area of wire bent in the shape of the square has more area than the rectangle.
Hence, the given statement is true and option 1 is correct.

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