Question

The area of rectangle gets reduced by 80 sq units if its length is reduced by 5 units and breadth is increased by 2 units.if we increase the increase the length by 10 units and decrease the breadth by 5 units,the area will increase by 50 sq units. Find the length and of the rectangle​

Answer 1

GIVEN :-

• The area of rectangle gets reduced by 80 sq units , if its length is

       reduced by 5 units and breadth is increased by 2 units .

• The area of rectangle gets increased by 50 sq units , if its  length is

       increased by 10 units and breadth is reduced by 5 units .

TO FIND :-

• Length of rectangle .

• Breadth of rectangle .

SOLUTION :-

Let ,

Length = x

Breadth = y

Area = xy

According to the first condition ,

 $\longrightarrow\sf (x-5)(y+2) = xy - 80\\\\\longrightarrow xy+2x-5y-10=xy-80\\\\\longrightarrow 2x-5y = -80+10 \\\\\longrightarrow 2x-5y = -70 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

According to the second condition ,

  $\longrightarrow \sf (x+10)(y-5)=xy+50 \\\\\longrightarrow xy-5x+10y-50 = xy+50 \\\\\longrightarrow -5x+10y = 50+50\\\\\longrightarrow -5x+10y = 100 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

 

 Equation (1) × 5 ,

 $\longrightarrow \sf 10x-25y = -350 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(3)$

 Equation (2) × 2 ,

 $\longrightarrow \sf -10x+20y = 200 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(4)$

Add equation (3) and equation (4) ,

 $\longrightarrow\sf -5y = -150 \\\\\longrightarrow 5y = 150 \\\\\longrightarrow\bf y = 30$

 

 Substitute y = 30 in equation (1) ,

  $\longrightarrow\sf 2x-5\times 30 = -70\\\\\longrightarrow 2x - 150 = -70 \\\\\longrightarrow 2x= 80\\\\\longrightarrow \bf x = 40$

Length of the rectangle = 40 units

Breadth of the rectangle = 30 units