Question

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is
increased by 3 cm, the area of the new rectangle is the same as the original rectangle. Find the length and
breadth of the rectangle.​

Answer 1

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and breadth of the original rectangle.

Answer 2

Answer:

Let consider the breadth of the rectangle be x.

And,Length be (x+7)cm

According to the condition:

(x+3)(x+3)=x(x+7)

$⇒ {x}^{2} + 9 + 6x = {x}^{2} + 7x \\ \\ ⇒ {x}^{2} - {x}^{2} + 6x - 7x = - 9$

$⇒x = 9$

Now,

Length= (x+7)cm = 9+7=16cm

Breadth= 9cm.

Therefore, The length of the rectangle is 16cm and breadth is 9cm.