Question

If the area of a square increases by $69\%$, then the side of the square increase by:

• A. $13\%$
• B. $30\%$
• C. $39\%$
• D. $69\%$

Answer 1

The correct option is B $30\%$

Let the initial area be $l^2$ for square of side length $l$.

Then if initial area is increased by $69\%$ we have, new area as,

$(l{)}^2=l^2+\frac{69}{100}{l}^2$

(where $l^{\prime }$ is the new side length )

$\Rightarrow (l^{\prime }{)}^2=\frac{100+69}{100}{l}^2$

$\Rightarrow (l^{\prime }{)}^2=\frac{169}{100}{l}^2$

$\Rightarrow l^{\prime }=\frac{13}{10}l$

$\Rightarrow l^{\prime }=l+\frac{3}{10}l$

$\Rightarrow l^{\prime }=l+\frac{30}{100}l$

So, length is increased by $30\%$