Question

The length of a rectangle is greater than the breadth by 3cm.if the length is increased by 9cmand the breadth is readuced by 5cm,the area remains the same.find the dimensions of the rectangle

Answer 1

$\huge\bf\green {Hey \: there !}$


▶ Given :


i) Length of the rectangle is greater than the breadth by 3 cm.


ii) If the length is increased by 9 cm and the breadth is reduced by 5 cm, the area remains the same.



▶ Let :


i) Breadth of the rectangle = x m



▶ To Find : The dimensions of the rectangle



▶According to the Question :


Length of the rectangle = ( x + 3 ) m


•°• Area of the rectangle = Length × Breadth


=> ( x + 3 ) ( x )


=> ( x^2 + 3x ) m^2


•°• Area of the rectangle = ( x^2 + 3x ) m^2


The length breadth is increased by 9 cm and the breadth is reduced by 5 cm. Thus we have :


Length = ( x + 3 + 9 ) m


Length = ( x + 12 ) m


Breadth = ( x - 5 ) m



•°• New area = ( x + 12 ) ( x - 5 )


=> ( x^2 - 5x + 12x - 60 ) m^2


=> ( x^2 + 7x - 60 ) m^2


•°• New area = ( x^2 + 7x - 60 ) m^2



The new area and original area are equal. Thus, we have :


=> x^2 + 3x = x^2 + 7x - 60


=> x^ 2 + 3x - x^2 - 7x = - 60


=> - 4x = - 60


$\huge\color {green} \boxed{\mathbb{x = 15 }}$


Hence, the length and breadth of the rectangle are 18 and 15 respectively.


✔✔ Hence, it is solved ✅✅



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