Question

If perimeter of a square is tripled, then area will be ______ of original area.

• A. $4$ times
• B. $\frac{1}{4}$ times
• C. $9$ times
• D. $\frac{1}{9}$ times

Answer 1

The correct option is C $9$ times

$P=4\times S=4S$

$P_{new}=4\times S^{\prime }=4S^{\prime }$

$P_{new}=3P$

Thus, $4S^{\prime }=12S$

$S^{\prime }=3S$

$A=S^2$

$A^{\prime }=(S^{\prime }{)}^2$

$A^{\prime }=(3S{)}^2$

$⟹A^{\prime }=9A$