Question

A wire is in the shape of a square of side is10m . If the wire is rebent into a rectangle of length 12m find its breadth.which encloses more area

Answer 1

$perimetre \: of \: square = 4 \times 10 = 40 {m}$
$perimetre \: of \: rectangle \: = 2(l + b) \\ = 2(12 + b) = (24 + 2b)m$
$now \\ perimetre \: of \: square = perimetre \: of \: rectangle$
$therefore \\ 24 + 2b = 40 \\ 2b = 40 - 24 = 16 \\ b = 8$
$so \: the \: breadth \: of \: the \: rectangle \: is \: 8 m$
$area \: of \: square = 10 \times 10 = 100 {m}^{2}$
$area \: of \: rectangle \: = 12 \times 8 = 96 {m}^{2}$

$therefore \: the \: square \: encloses \: a \: larger \: area$