Question

If the length of a rectangle is decreased by 2 metres and the breadth increased by 2 metres and the area would increase 8 square metres .If the length is decreased by 3metres and the breadth decreased by 1 metre,the area would decrease by 27 metres.what are the length and breadth

Answer 1

SOLUTION :-

Let,

Length of the rectangle = x

Breadth of the rectangle = y

Area = xy

According to the first condition,

$\longrightarrow\sf (x-2)(y+2) = xy+8 \\\\\longrightarrow xy+2x-2y-4 = xy + 8 \\\\\longrightarrow 2x-2y = 12 \\\\\ \longrightarrow x-y = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According the second condition,

$\longrightarrow \sf (x-3)(y-1)= xy - 27 \\\\\longrightarrow xy-x-3y+3 = xy - 27 \\\\\longrightarrow -x-3y = -30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Add eq(2) and eq(1),

$\longrightarrow\sf -4y = -24 \\\\\longrightarrow \bf y = 6$

Substitute the value of y in eq(1),

$\longrightarrow\sf x-6 = 6 \\\\\longrightarrow\bf x = 12$

Length of the rectangle = 12 m

Breadth of the rectangle = 6 m