Question

The area of a rectangle gets reduced by 9 square unit, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Answer 1

Answer:

Step-by-step explanation:

Let the length be x

& the breadth be y

Then area will be xy

• According to question
• CASE I

       (x-5)(y+3)=xy-9

        xy+3x-5y-15=xy-9

         3x-5y=6

            x=$\frac{6+5y}{3}$              (1)

• CASE II

       (x+3)(y+2)=xy+67

        xy+2x+3y+6=xy+67

           2x+3y=61

               x=$\frac{61-3y}{2}$           (2)

• Equating (1) & (2)

      $\frac{6+5y}{3}$=$\frac{61-3y}{2}$

       2(6+5y)=3(61-3y)

       12+10y=183-9y

       12-183=-9y-10y

       -171=-19y

      y=$\frac{-171}{-19}$

      y=9m

• From Equation (1)

        x=$\frac{6+5(9)}{3}$

        x=$\frac{51}{3}$

        x=17m

Answer 2

Answer:

Hope it helps

Thank you....