Question

If the breadth of a rectangle is increased by 3cm and the length is reduced by 2cm, its area
would increased by 20 sq.cm. But if the breadth is reduced by 2cm and the length is
increased by 1cm, the area would be reduced by 24 sq. cm. Find the length and the breadth
of the rectangle​

Answer 1

SOLUTION :-

Let,

Length = x

Breadth = y

Area = xy

According to first condition,

$\longrightarrow\sf (x-2)(y+3)= xy+20\\\\\longrightarrow\sf xy+3x-2y-6 = xy + 20 \\\\\longrightarrow 3x-2y = 20+6 \\\\\longrightarrow 3x - 2y = 26 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .........................(1)$

According to the second condition,

$\longrightarrow\sf (x+1)(y-2)=xy-24 \\\\\longrightarrow xy-2x+y-2 = xy - 24 \\\\\longrightarrow -2x+y = -24+2\\\\\longrightarrow -2x+y = -22 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .........................(2)$

Equation (2) × 2,

$\longrightarrow\sf -4x+2y = - 44 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .........................(3)$

Add equation (1) and equation (2),

$\longrightarrow \sf -x = -18 \\\\\longrightarrow \bf x = 18$

Substitute x = 18  in equation (2),

$\longrightarrow \sf 3 \times 18-2y = 26 \\\\\longrightarrow 54-2y = 26 \\\\\longrightarrow -2y = 26-54 \\\\\longrightarrow -2y = -28 \\\\\longrightarrow\bf y = 14$

Length of the rectangle = 18 cm

Breadth of the rectangle = 14 cm