Question

A pavement of 2m of wide runs around a square ground.the total area of the ground and pavement is 1225m^2.what is the area of the ground?

Answer 1

$\bold{let : } \: \\ \\\bold {the \: side \: of \: that \: square \: ground : } \\ \\ \bold{x \: m} \: \\ \\ \\ \\ \bold{area \: of \: that \: ground : } \\ \\ \bold {{x}^{2} {m}^{2} } \\ \\ \\ \\\bold {side \: of \: ground \: with \: pavement : } \\ \\ \bold{ ({x + 2})^{2} } \\ \\ \\ \\ \bold{area \: of \: ground \: with \: pavement : } \\ \\ \bold{({x + 2})^{2} } \\ \\ {x}^{2} + 4x + {2}^{2} \\ \\ {x}^{2} + 4x + 4 \\ \\ \bold{but \: we \: have \: given \: it \: } \\ \\ 1225 = {x }^{2} + 4x + 4 \\ \\ {x}^{2} + 4x + 4 - 1225 = 0 \\ \\ {x}^{2} + 4x - 1221 = 0 \\ \\ \bold{by \: factorisation \: method} \\ \\ {x}^{2} + 33x - 29x - 1221 = 0 \\ \\ x(x + 33) - 29(x + 33) = 0 \\ \\ (x + 33) = 0 \: or \: (x - 29) = 0 \\ \\ \bold{x = - 33\: m} \: or \: \bold{x = 29 \:m} \\ \\ \\ \\ \bold{but \: side \: can \: not \: be \: negative} \: \\ \\ x \: = 29 \\ \\ \\ \\ \bold{area \: of \: ground :} \\ \\ ( {x})^{2} \\ \\ {29 \:m}^{2} \\ \\ \bold{729 \:{m}^{2}}$