Question

if in a rectangle, thelength is increased and the breadth is reduced by 2 units each,the area is reduced by 28 square units. if the length is reduced by 1 unit and the breadth is increased by 2 unit, the area is increased by 33 square units. find the dimensions of the rectangle.​

Answer 1

SOLUTION :-

Let,

Length of the rectangle = x

Breadth of the rectangle = y

Area = xy

According to the first condition,

$\longrightarrow \sf (x+2)(y-2) =x y - 28 \\\\\longrightarrow xy-2x+2y-4 = xy - 28 \\\\\longrightarrow -2x+2y = -28+4 \\\\\longrightarrow -2x+2y = -24 \\\\\longrightarrow -x+y = -12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(1)$

According to the second condition,

$\longrightarrow\sf (x-1)(y+2) = xy + 33\\\\\longrightarrow xy+2x-y-2 = xy + 33\\\\\longrightarrow 2x-y = 33+2 \\\\\longrightarrow 2x- y = 35 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

Equation (2) + Equation (1),

$\longrightarrow \bf x = 23$

Substitute the value of x in equation (1),

$\longrightarrow \sf -23 + y = -12 \\\\\longrightarrow y = -12+23 \\\\\longrightarrow \bf y = 11$

Length of the rectangle = 23 cm

Breadth of the rectangle = 11 cm