Question

The length of one pair of opposite sides of a square is reduced by 10 % and that of the other pair is increased by 10 %. Find the ratio of the area of the new rectangle to the area of the original square

• A. $\frac{1}{100}$
• B. $\frac{49}{50}$
• C. $\frac{99}{100}$
• D. $\frac{1}{50}$

Answer 1

The correct option is C $\frac{99}{100}$

Let the side of the square be a
$\therefore$ Increased length $=a+10$ % of $a=\frac{11a}{10}$
Decreased length $=a-10$% of $a=\frac{9a}{10}$
Area of original square $=a^2$

Area of the new rectangle $=\frac{11a}{10}\times \frac{9a}{10}=\frac{99a^2}{100},i.e.$

Difference of the two areas $=a^2-\frac{99a^2}{100}=\frac{a^2}{100}\Rightarrow$

$\Rightarrow$ The area of the new rectangle is $1$ less than the area of original square