Question

Find the value of $(105{)}^2$ by visualizing the identity $(a+b{)}^2=a^2+2ab+b^2$.

• A. $10,025$
• B. $11,025$
• C. $12,025$
• D. $9,025$

Answer 1

The correct option is B $11,025$

We have to find value of $(105{)}^2$. So, let us visualize this with the help of diagram.


$105$ can also be written as $(100+5)$.

So, the value of $(105{)}^2$ will be area of square WXYZ.

$\Rightarrow$Area of square WXYZ $=(100+5)(100+5)=(100+5{)}^2$sq.units.

It can also be written as
Area of square WXYZ = Area of Yellow square + Area of Brown and Green rectangles + Area of White square

Brown and green rectangles have similar dimensions.

So, area of brown and green rectangles $=(100\times 5)$ sq.units.

Area of white square is $=(5\times 5)$ sq.units.

And, Area of yellow square $=(100\times 100)$ sq.units

Now, $\Rightarrow (100+5{)}^2=100\times 100+100\times 5+100\times 5+5\times 5)$

$\Rightarrow (100+5{)}^2=(100{)}^2+2\times 100\times 5+5^2$

$\Rightarrow (100+5{)}^2=10,000+1,000+25=11,025.$sq.units.

$\Rightarrow (105{)}^2=11,025$

$\therefore$ Required value of $(105{)}^2$ is $11,025$.