Question

side of a square picture is 2x metre. If a footpath 5m wide is constructed around it , what is the area of the field including the path .

Answer 1

$Given \: side \: of \: a\: square \:field (a) = 2x \:m$

$i )\blue { Area \: of \: square\:field}\\ = a^{2} \\= (2x \: m)^{2} \\= 4x^{2} \: m^{2} \: ---(1)$

$Width \: of \: a \: footpath (w) = 5 \:m$

$</p><p>/* If a footpath is constructed around the field then */</p><p>[tex] Side \: of \: of \: new \: square (s) = a + 2w \\= 2x + 2\times 5 \\=( 2x + 10 )\: m$

$ii )Now, \red { Area \: of \: the \: field \: including}\\\red{ path} = s^{2}\\= (2x+10)^{2} \\= (2x)^{2} + 2 \times 2x \times 10 + 10^{2} \\= (4x^{2} + 40x + 100 ) m^{2} \: --(2)$

$iii) \pink { Area \: of \: the \: footpath } \\= (2) - (1) \\= (4x^{2} + 40x + 100 ) m^{2} - 4x^{2} \:m^{2}\\=( 40x + 100)\: m^{2} \: --(3)$

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