Question

Sanjay has a square mirror measuring $10cm$ by $10cm$.Silvie has a square mirror which covers twice the area of Sanjay's mirror. Determine the dimension of Silvie's mirror correct to $2$ decimal places.

Answer 1

Hint: First, we shall analyze the given information so that we can able to solve the problem. It is given that Sanjay’s square mirror consists of $10cm$ by $10cm$ dimension and the side of the square is $10cm$. We are given a condition that Silvie’s square mirror covers twice the area of Sanjay’s square mirror.
We shall apply the formula of the area of the square in this question to obtain the required answer.
Formula to be used:
The formula to calculate the area of the square is as follows.
Area of the square, $A = a \times ac{m^2}$
Where $a$ is the side of the square.

Complete step by step answer:
It is given that Sanjay’s square mirror consists of $10cm$ by $10cm$dimension.
Hence the side of the square is $10cm$.
Now, we shall calculate the area of the square using the formula $A = a \times ac{m^2}$
Thus area of Sanjay’s square mirror $ = 10 \times 10c{m^2}$
                                                                $ = 100c{m^2}$
We are given a condition that Silvie’s square mirror covers twice the area of Sanjay’s square mirror.
That is the area of Silvie’s square mirror$ = 2 \times $area of Sanjay’s square mirror
                                                   $ = 2 \times 100$
                                                    $ = 200c{m^2}$
We are asked to calculate the dimension of Silve’s square mirror.
Let $x$ be the side of the required square mirror.
Now, we shall use the area of the square using the formula $A = a \times ac{m^2}$
Area of Silvie’s square mirror $ = x \times x$
       $ \Rightarrow 200 = {x^2}$
Taking square roots on both sides, we have
 $ \Rightarrow \sqrt {200} = \sqrt {{x^2}} $
$ \Rightarrow \sqrt {2 \times 2 \times 2 \times 5 \times 5} = x$
$ \Rightarrow 2 \times 5 \times \sqrt 2 = x$
$ \Rightarrow 2 \times 5 \times 1.414 = x$ $\left( {\sqrt 2 = 1.414} \right)$
$ \Rightarrow 10 \times 1.414 = x$
$ \Rightarrow x = 14.14cm$
Hence, the dimension of Silve’s square mirror is $14.14cm$ by $14.14cm$

Note: The side of the square and the dimension of the side is not the same. The side of the square refers to a single value whereas the dimension of the square contains two or more than two values. That is if $a$ is the side of the square, the dimension of the square will be $a$ cm by $a$ cm. Hence, the square is said to be a two-dimensional figure.