# 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?

R Riya

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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