Question

the length of a rectangular field is 11m more than its width.if the length is decreased by 12 m and the width is increased by 10m, the area decreases by 24m2.find the length and width of the field​

Answer 1

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Answer 2

$\huge\underline\bold\blue{Question \: : }$

The length of a rectangular field is 11m more than its width. If the length is decreased by 12m and the width is increased by 10m , the area decreases by 24m². Find the length and the width of the field.

$\huge\underline\bold\red{Solution \: : }$

$\sf{{Let \: the\:width }{ \:of \: the \: field \: be \: \: x \: m. }}$

$\sf{{ Then\:, \: the\:length \: of \: }{the \: field \: is \:(x + 11) \: m \: and \: the \: area \: of \: the \: field \: is \: x(x + 11) \: m² }}$

$\sf{{The \: length \:of \:the \: new }{ \:field \: is \: [(x + 11) - 12] \: m \: = (x - 1)m \: and \: the \: width \: of \: the \: new \: field \: is \: (x + 10)m. }}$

$\sf{{Area \: of\:the \: }{new \: field \: = (x - 1)(x + 10)m²}}$

$\sf{{From \: the\: }{question, \: }}$

$\sf{{x(x + 11) - (x - 1)(x + 10) = 24\: \: }{ \: or \: \: x² + 11x - (x² + 9x - 10) = 24}}$

$\sf{{or \: \: \:2x + 10 = 24 }{\: \: \: \: or \: \: \: \: 2x = 24 - 10 = 14 \: \: \: or \: \: \frac{14}{2} = 17}}$

$\sf{{Therefore, \: \:x + 11 \: =7 + 11 }{ \: = 18 }}$

$\sf{{Hence, \:the \: width \:of }{ \:the \: field \: is \: 7m \: and \: its \: length \: is \: 18m. }}$

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$\sf{{Hope \: it\: }{helps \: you....♡}}$