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 area of the original rectangle. Find the length and breadth of the original rectangle.

Answer 1

Let the breadth of the rectangle be $x$ cm.

Therefore, length $=x+7$ cm

According to the question,

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

$x^2+9+6x=x^2+7x$

$x=9$

Hence, dimensions of original rectangle,

Length = $16cm$

Breadth = $9cm$