Question

The perimeter of a rectangular plot is 36 m. If the length is increased by 6m and the breadth is decreased by
3m, the area of the plot remains the same, what is the length of the plot?​

Answer 1

Dimensions of a rectangular plot:

$Let \: Length = l \: m \: and \: breadth = b \: m$

$i) Perimeter \: of \: the \: plot = 36 \: m$

$\implies 2( l + b ) = 36$

$\implies l + b = \frac{36}{2}$

$\implies b = 18 - l \: --(1)$

$ii ) Area \: of\: the \: plot = l \times b \: --(2)$

/* According to the problem given */

$If \: the \: length \: is \: increased \: by \: 6\:m\\and \: the \: breadth \: is \: decreased \: by \\ 3\:m\: then$

New Dimensions of the rectangular plot:

$Length = ( l + 6 )\: m \: and \\breadth = ( b - 3 ) \: m$

$Area \: of \: the \: new \: plot = ( l+6)(b-3) \:--(3)$

$\pink{ (l+6)(b-3) = l \times b }$

$\implies l( b-3) + 6( b -3 ) = lb$

$\implies \cancel {lb} - 3l + 6b - 18 =\cancel { lb}$

$\implies -3l + 6b - 18 = 0$

/* Dividing each term by 3 , we get */

$\implies - l + 2b - 6 = 0$

$\implies - l + 2( 18 - l ) = 6\: [ From \: ( 1 ) ]$

$\implies - l + 36 - 2l = 6$

$\implies - 3l = 6 - 36$

$\implies -3l = -30$

$\implies l = \frac{ -30}{-3}$

$\implies l = 10$

Therefore.,

$\red{ Length \: of \: the \: plot } \green { = 10\:m }$

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Answer 2

Answer:Could vary in this scenario 18

Step-by-step explanation:

If the perimeter is 36 in total we can split it up into four even parts (square) or two smaller parts and two bigger parts (rectangle)I chose the ladder. For square it can be 9 on all sides or rectangle where it can be 12 on two sides and six on the smaller sides.

so I can decrease 6 by 3 and increase 12 by 6 or flip way round would be the same. We get 18 on one side and 3 on the other

Hope this helps! rate whatever you want