Question

the length of a rectangle is 4 centimetre more than its breadth if the length is increased by 4 cm and breadth is decreased by 2 centimetre the area image the same as that of original rectangle find the length and breadth of the rectangle

Answer 1

$Let\ the\ breadth\ and\ the\ length\ of\ the\ rectangle\ be\ x\ and\ x+4 \\ respectively. \\ \\ The\ breadth\ and\ the\ length\ of\ the\ new\ rectangle\ will\ be\ x-2\ and \\ x+8\ respectively. \\ \\ x(x+4) = (x-2)(x+8) \\ \\ = x^2+4x = x^2+6x-16 \\ \\ \\ 4x = 6x-16 \\ \\ 6x-4x = 16 \\ \\ = 2x = 16 \\ \\ x = \frac{16}{2} = 8$

$\\ \\ Breadth\ of\ the\ rectangle = x = \bold{8\ cm} \\ \\ Length\ of\ the\ rectangle = x+4 = 8+4 = \bold{12\ cm} \\ \\ \\ Breadth\ of\ the\ new\ rectangle = x-2 = 8-2 = \bold{6\ cm} \\ \\ Length\ of\ the\ new\ rectangle = x+8 = 8+8 = \bold{16\ cm}$

$8 \times 12 = 96\ cm^2 \\ \\ 6 \times 16 = 96\ cm^2$

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Answer 2

$\bf{\underline{\huge{ANSWER}}}$


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