Answer:
The perimeter of the square is;
[tex]16\sqrt[]{5}[/tex]
Explanation:
Given that the diagonal of a square is;
[tex]d=4\sqrt[]{10}[/tex]
we can draw the square as;
Using Pythagoras theorem;
[tex]\begin{gathered} x^2+x^2=d^2 \\ 2x^2=d^2 \\ 2x^2=(4\sqrt[]{10})^2 \\ 2x^2=160 \\ x^2=\frac{160}{2} \\ x^2=80 \\ x=\sqrt[]{80} \\ x=4\sqrt[]{5} \end{gathered}[/tex]
The perimeter of a square is the sum of the four equal sides;
[tex]\begin{gathered} P=4\times x=4(4\sqrt[]{5}) \\ P=16\sqrt[]{5} \end{gathered}[/tex]
Therefore, the perimeter of the square is;
[tex]16\sqrt[]{5}[/tex]
