Question

Area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 unit we increase the length by 3 unit and breadth by two unit the area increased by 64 square unit find the dimensions of the rectangle

Answer 1

let the length of the rectangle = x units

and breadth of the rectangle =y units

therefore, area = xy square units

A. T. Q.

(x-5)(y+3)=(xy-9)

xy +3x -5y -15 =xy -9

3x -5y =-9 +15

3x -5y =6. ..........(1)

(x+3)(y+2) = xy+67

xy +2x +3y +6 =xy +67

2x+3y =67-6

2x+3y =61. ..........(2)

multiplying equation (1) by 2 and equation (2)by 3 and then subtracting

6x - 10y = 12

6x +9y =183

- - -

....................

-19y =-171

......................

y =9

putting the value of y in eq 1

3x -5(9) =6

3x -45 =6

3x =6+45

3x =51

x =17

Thus, the length of rectangle =17 units

and breadth of rectangle =9 units

therefore, it's area =17 *9

= 153