Question

The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m^2.Find its dimensions​

Answer 1

${ \red{ \bf{ In \: first \: case:}}}$

${ \red{ \bf{ Let \: the \: length \: of \: the \: rectangle \: be \: ‘x’ \: m., }}}$

Width = (x – 5) meter

Area = lb

= x(x – 5) sq.m

${ \red{ \bf{ In \: second \:case: }}}$

Length = (x – 9) meter

Width = 2 (x – 5) meter

Area = (x – 9) 2(x – 5) = 2(x – 9) (x – 5) sq.m

${ \red{ \bf{ So \: according \: to \: the \: question,}}}$

2(x – 9) (x – 5) = x(x – 5) + 140

2(x2 – 14x + 45) = x² – 5x + 140

2x2 – 28x + 90 – x² + 5x – 140 = 0

x² – 23x – 50 = 0

${ \red{ \bf{ Let \: us \: factorise, }}}$

x² – 25x + 2x – 50 = 0

x(x – 25) + 2 (x – 25) = 0

(x – 25) (x + 2) = 0

${ \red{ \bf{ So, }}}$

(x – 25) = 0 or (x + 2) = 0

x = 25 or x = -2

${ \red{ \bf{ ∴ Length \: of \: the \: first \:rectangle = 25meters. }}}$

${ \red{ \bf{ [Since, \: -2\: is\: a \: negative \: value]}}}$

Width = x – 5 = 25 – 5 = 20meters

Area = lb

${ \red{ \bf{ = 25 × 20 = 500 m² }}}$