• # question_answer If the base of a rectangle is increased by 10% and the area is unchanged, then its corresponding altitude must be decreased by? A)  $11\frac{1}{9}%$                    B)  $9\frac{1}{11}%$        C)         11%                 D)         10%

Let the length = 100 m and       height = x m Area = 100 x New length = 110 m and let new height $=(x-y%\,\,\text{of}\,x)$ Then,     $110\times \,\left( x-\frac{y}{100}\cdot x \right)=100\times x$ $\Rightarrow$   $110\times \left( 1-\frac{y}{100} \right)=100$ $\Rightarrow$   $1-\frac{y}{100}=\frac{100}{110}$ $\Rightarrow$   $\frac{y}{100}=1-\frac{100}{110}=\frac{10}{110}=\frac{1}{11}$ $\therefore$      $y=\frac{1000}{11}=9\frac{1}{11}%$