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  • A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square. what will be the measure of each side. Also find which shape encloses more area?

Q. 6.     A wire is in the shape of a rectangle. Its length is 40\; cm and breadth is 22\; cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

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It is given that the length of rectangular wire is 40\; cm and breadth is 22\; cm.

Now, if it reshaped into a square wire

Then,

The perimeter of rectangle = perimeter of the square

2(l+b)= 4a

\Rightarrow 2(40+22) = 4a

\Rightarrow a = \frac{124}{4}= 31 \ cm

Now,

Area of rectangle = l \times b = 40 \times 22 = 880 \ cm^2

Area of square = a^2 = (31)^2 = 961 \ cm^2

Therefore, the side of the square is 31 cm and we can clearly see that square-shaped wire encloses more area

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Riya

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