Question

The Area of rectangle reduces by 20m^2, if its length is increased by 1m and the breadth is reduced by 2m. The area increases by 12m^2, if the length is reduced by 3m and breadth is increased by 4m. Find the dimensions of the rectangle.​

Answer 1

$\boxed{\huge{\red{Answer}}}$

$\longrightarrow$Let length of rectangle = x

$\longrightarrow$Let breadth of rectangle = y

$\boxed{\huge{ATQ-1}}$

$\longrightarrow$( x + 1 ) ( y - 2 ) = xy - 20m²

$\longrightarrow$xy - 2x + y - 2 = xy - 20

$\longrightarrow$ -2x + y = - 18

$\longrightarrow$2x - y = 18 -------------( 1 )

$\boxed{\huge{ATQ-2}}$

$\longrightarrow$( x - 3 ) ( y + 4 ) = xy + 12m²

$\longrightarrow$xy + 4x - 3y - 12 = xy + 12

$\longrightarrow$ 4x - 3y = 24 ------------ ( 2 )

$\mathsfrack{Multiply\:by\:2\:to\:eqn\:(1)}$

$\longrightarrow$4x - 2y = 36------------ ( 3 )

By comparing ( 3 ) and ( 2 )

4x - 3y = 24

4x - 2y = 36

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Sign changes

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$\longrightarrow$ - y = - 12

$\longrightarrow$ y = 12

Put y in eqñ ( 1 )

$\longrightarrow$2x - 12 = 18

$\longrightarrow$ x = \frac{30}{2}

$\longrightarrow$ x = 15

Length of rectangle$\longrightarrow$15m

Breadth of rectangle$\longrightarrow$12m