A wire is in shape of a rectangle. Its length is $40 c m$ and breadth is $22 c m$ . If the same wire is reshaped into a square, what will be the measure of each side. Also find which shape encloses more area.

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Solution

Given,
Length of rectangle $(l) = 40 c m$
Breadth of rectangle $(b) = 22 c m$

Perimeter of rectangle $= 2 (l + b)$
$= 2 (40 + 22) c m$
$= 124 c m$
It is reshaped into square

$∴$ Perimeter remains same
Let, the edge of square be $a$
$∴ 4 a = 124$
$\Rightarrow a = 31$

Hence, the side of square is $31 c m$ .

Area of rectangle $= l \times b$
$= 40 \times 22 s q . c m$
$= 880 s q . c m$

Area of square $= S i d e \times S i d e$
$= 31 \times 31 s q . c m$
$= 961 s q . c m$

Hence, the square encloses more area.

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