Question

The length of a rectangle is increased by one-third and the breadth is reduced by one-third. The area of the rectangle is reduced b​

Answer 1

$\text{let the original length and breadth of the}$

$\text{Rectangle be l and b units}$

$\text{Then,the original area will be l \times b units^{2}}$

$New\: breadth = l + \dfrac{1}{3}l = \dfrac{4}{3}l$

$New\: length = b - \dfrac{1}{3}b = \dfrac{2}{3}lb$

$\therefore New Area = \dfrac{4}{3}l × \dfrac{2}{3}b = \dfrac{8}{9}lb unit^{2}$

$Decrease\:in\:Area$

$\Rightarrow\bigg(\dfrac{lb - \dfrac{8}{9}lb}{lb} × 100\bigg)$%

$\Rightarrow\dfrac{\dfrac{1}{9}lb}{lb} × 100 = 11\dfrac{1}{9}$%