Question

if the length of a rectangular field is increased by 5m and its breadth decreased by 5m ,its area decreased by 50m^2 if both length and breadth are increased by 5m its area increased by 200m^2.find its length and breadth​

Answer 1

SOLUTION :-

Let,

Length of the rectangle = x

Breadth of the rectangle = y

Area = xy

According to the first condition,

$\longrightarrow\sf (x+5)(y-5) = xy - 50 \\\\\longrightarrow xy-5x+5y-25 = xy - 50 \\\\\longrightarrow -5x+5y = -25 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ . .........(1)$

According to the second condition,

$\longrightarrow\sf (x+5)(y+5)= xy + 200 \\\\\longrightarrow xy+5x+5y+25 = xy + 200 \\\\\longrightarrow 5x+5y = 175 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ . .........(2)$

Add eq(1) and eq(2),

$\longrightarrow\sf 10y = 150 \\\\\longrightarrow \bf y = 15$

Substitute the value of x in eq(2),

$\longrightarrow \sf 5x + 5\times 15 = 175 \\\\\longrightarrow 5x+75 = 175 \\\\\longrightarrow 5x = 100 \\\\\longrightarrow\bf x = 20$

Length of the rectangle = 20 m

Breadth of the rectangle = 15 m