Question

If the diagonal of a square is increased by $35\%$, then find the percentage increases in the area of the square

• A. $80.2$ $\%$
• B. $85.5$ $\%$
• C. $92.25$ $\%$
• D. $82.25$ $\%$

Answer 1

Answer: (D)

$82.25$ $\%$

Since diagonal = $\sqrt{2}a$
If the diagonal increased by $35\%$, then $a$ also increases by $35\%$.
Therefore, $a^{\prime }=a+0.35a=\left(1.35\right)a$
$\therefore {\left(a^{\prime }\right)}^2={\left(1.35a\right)}^2=1.8255$ $a^2$
$\therefore$ Change $=0.8225a^2$
$\therefore$ Increase in area $=82.25\%$.