Question

The diagonals of a square are $4$ meters long.

The side of this square is equal to the diagonal of a second square. find the side of the second square.

Answer 1

Find the length of the second square:

The length of the diagonal of the first square is $4$ meters.

Let $s_2$ be the side of the second square.

Since all four sides of the square are equal $s$ and the length of each diagonal of the square is $s\sqrt{2}$.

So, the length of the diagonal of the second square will be $s_2\sqrt{2}$.

According to the question,

The side of the first square is equal to the diagonal of a second square.

So, the side of the first square will be $s_2\sqrt{2}$.

Now, the length of the diagonal of the first square is $4$.

Therefore, length of second square is calculated as:

$\begin{array}{rcl}{s}_2\sqrt{2}\times \sqrt{2}& =& 4\\ & \Rightarrow & 2s_2=4\\ & \Rightarrow & s_2=2\end{array}$

Hence, the side of the second square is $\mathbf{2}$ meters.