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Hint : Create equations on the basis of given conditions.

Let the length of the rectangle be $x$ metres and the breadth be $y$ metres.

Area of the rectangle $ = length \times breadth = x \times y = xy$ sq. metres

From the given information, we have,

\[(x + 3) \times (y - 4) = xy - 67\]

& \[(x - 1) \times (y + 4) = xy + 89 \\\]

$

(x + 3) \times (y - 4) = xy - 67 \\

= > xy - 4x + 3y - 12 = xy - 67 \\

= > 4x - 3y = 55 \\

= > 4x = 3y + 55....(i) \\

$

Also,

$

(x - 1) \times (y + 4) = xy + 89 \\

= > xy + 4x - y - 4 = xy + 89 \\

= > 4x - y = 93....(ii) \\

$

Substituting equation (i) in equation (ii), we get,

$

4x - y = 93 \\

= > 3y + 55 - y = 93 \\

= > 2y = 38 \\

= > y = 19 \\

$

Substituting $y = 19$ in equation (i), we get,

$

4x = 3y + 55 \\

= > 4x = 3(19) + 55 \\

= > 4x = 112 \\

= > x = 28 \\

$

Therefore, the length of the rectangle $ = x = 28$ metres.

breadth of rectangle $ = y = 19$ metres.

Note â€“ In this problem, first let assume the breadth and length of the rectangle then follow the given conditions which gives us two equations. On solving these two equations, we get the final answer.

Let the length of the rectangle be $x$ metres and the breadth be $y$ metres.

Area of the rectangle $ = length \times breadth = x \times y = xy$ sq. metres

From the given information, we have,

\[(x + 3) \times (y - 4) = xy - 67\]

& \[(x - 1) \times (y + 4) = xy + 89 \\\]

$

(x + 3) \times (y - 4) = xy - 67 \\

= > xy - 4x + 3y - 12 = xy - 67 \\

= > 4x - 3y = 55 \\

= > 4x = 3y + 55....(i) \\

$

Also,

$

(x - 1) \times (y + 4) = xy + 89 \\

= > xy + 4x - y - 4 = xy + 89 \\

= > 4x - y = 93....(ii) \\

$

Substituting equation (i) in equation (ii), we get,

$

4x - y = 93 \\

= > 3y + 55 - y = 93 \\

= > 2y = 38 \\

= > y = 19 \\

$

Substituting $y = 19$ in equation (i), we get,

$

4x = 3y + 55 \\

= > 4x = 3(19) + 55 \\

= > 4x = 112 \\

= > x = 28 \\

$

Therefore, the length of the rectangle $ = x = 28$ metres.

breadth of rectangle $ = y = 19$ metres.

Note â€“ In this problem, first let assume the breadth and length of the rectangle then follow the given conditions which gives us two equations. On solving these two equations, we get the final answer.

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