Question

If each side of a square is increases by 2 units, then the new area is .

• A. $a^2+4a+4$
• B. $a^2+4a+2$
• C. $2a^2+4a+4$
• D. $a^2+2a+4$

Answer 1

The correct option is A $a^2+4a+4$

Let the side of the square be 'a' units.
Area of the square $=a^2$ -----(1)
After increasing 2 units, the side of the square = $(a+2)$units
Now, area of the square $=(a+2{)}^2$
Using the identity:
$(a+b{)}^2=a^2+b^2+2ab$
$=a^2+(2{)}^2+2\times a\times 2$
$=a^2+4a+4$