Question

In a square, doubling every side increases the area by $27$ Sq. units. What is the length of side of the newly formed square?

• A. $3$
• B. $6$
• C. $9$
• D. $18$

Answer 1

The correct option is B $6$

Let the side of a square be ${}^{\prime }{a}^{\prime }$ units then,

Area of square $=a^2$ sq.units

If each side of a square is doubled then,

Side of new square so formed $=2a$ units

Area of new square $=(2a{)}^2=4a^2$ sq.units

Increased Area $=4a^2-a^2=3a^2$ sq.units

According to the question,

$3a^2=27$

$a^2=\frac{27}{3}=9=3^2$

$a=3$ units

$\therefore$ Side of new square $=2\left(3\right)=6$ units

Option (B) Correct