Question

length of rectangle is greater than its breadth by 18cm. if both lenght and breadth are increased by 6cm, then area increased by 168cm2. find length and breadth.

Answer 1

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Answer 2

Let the breadth of the rectangle be x.

Then the length of the rectangle will be greater than the breadth by 18cm = (x+18) cm.

We know that Area of the rectangle = l * b

                                                             = x * (x + 18)

                                                             = x^2 + 18x ------------- (1)


Given that breadth of the rectangle is increased by 6cm. = (x+6)cm.

Then the length of the rectangle = (x + 6 + 18)

                                                        = (x + 24).

Now the area of the rectangle = (x + 6)(x + 24)
                    
                                                   = x^2 + 24x + 6x + 144

                                                   = x^2 + 30x + 144       ------------ (2)


On solving (1) and (2) with the increased area by 168cm^2.

x^2 + 18x + 168 = x^2 + 30x + 144

 18x + 168 = 30x + 144

12x = 24

x = 2.

If the breadth is 2cm Then the length will be (2 + 18) = 20cm.


Therefore the length = 20cm and the breadth = 2cm.


Hope this helps!