Question

the area of rectangle get reduced by 9m2 if its reduced by 5m and breadth is increase by 3cm and the breadth by 2m the area is increase by 67m2 .find the length and breadth of the rectangle

Answer 1

Let length of rectangle = x unitsAnd width of rectangle = y unitsArea of rectangle = length * width = x*yThe area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units.SoDecrease the length by 5 unit so new length = x - 5Increase the width by 3 unit so new width = y + 3New area is reduced by 9 unitsSo new area  = xy – 9Plug the value in formula length * width = area we get(x  - 5)(y + 3) = xy  - 9Xy  + 3x – 5y – 15  = xy – 9Subtract xy both side we get3x - 5y  = 6                 …(1)If we increase the length by 3units and the breadth by 2 units, the area increases by 67 square units.Increase the length by 3 unit so new length = x +3Increase the width by 2 unit so new width = y + 2New area is increased  by 67 unitsSo new area  = xy + 67Plug the value in formula length * width = area we get(x  +3)(y + 2) = xy  +  67Xy  + 2x  +  3y  +  6  = xy + 67Subtract xy both side we get2x  +  3y = 61                         …(2)*33x - 5y  = 6                 …(1)*2Cross multiply the coefficient of x we get6x + 9 y = 1836x -10y  =12Subtract now we get19 y = 171Y = 171/19 = 9Plug this value of y in equation first we get2x + 3* 9 = 612x  = 61 – 272x = 34X = 34/2 = 17