Question

The length of a rectangle is 5cm less than twice it's breadth. If the length is decreased by 3cm and breadth increased by 2cm, the perimeter of the resulting rectangle is 72cm. Find the area of the original rectangle.

Answer 1

Length of the rectangle is 5cm and twice of its beadth answer ia 20

Answer 2

Let the breadth of the rectangle be x cm.

Then the length of the rectangle will be 5 times less than twice it's breadth = (2x - 5) cm.

Given that the length is decreased by 3cm = (2x - 5 - 3)

                                                                         = (2x - 8).


Given that the breadth is increased by 2cm. = (x + 2).


Given that perimeter of the resulting rectangle = 72cm.

                                2(l + b) = 72

                                2(2x - 8 + x + 2) = 72

                                (2x - 8 + x + 2) = 36

                                (3x - 6) = 36

                                3x = 36 + 6

                                3x = 42

                                  x = 14cm.

The breadth of the original rectangle = 14cm.

The length of the original rectangle = (2x - 5)

                                                            = (2 * 14 - 5)

                                                            = (28 - 5)

                                                            = 23.


Therefore the area of the original rectangle = l * b

                                                                          = 23 * 14

                                                                          = 322 cm^2.

Hope this helps!