6. A wire is in shape of square of side 8cm. If the wire is rebent into rectangle of length 10cm find its breadth,which of these two shapes are larger in area.

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Solution

$s i d e l e n g t h o f s q u a r e = 8 c m$
$p e r i m e t e r o f s q u a r e = 4 \times 8 c m = 32 c m = l e n g t h o f t h e w i r e$
$n o w w i r e r e b e n t i n r e c t a n g u l a r s h a p e o f l e n g t h 10 c m$
$∴ p e r i m e t e r o f r e c t a n g l e = l e n g t h o f t h e w i r e = 32 c m$
$l e n g t h \times b r e a d t h = 32 c m$
$10 \times b = 32 c m$
$b = 3.2 c m$
$N o w a r e a o f s q u a r e = {s i d e}^{2} = 8 \times 8 {c m}^{2}$
$= 64 c m^{2}$
$a r e a o f r e c t a n g l e = l e n g t h \times b r e a d t h$
$= 10 \times 3.2 c m^{2}$
$= 32 c m^{2}$
$t h e r e f o r e, a r e a o f s q u a r e l a r g e r t h a n r e c t a n g l e$

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