Question

What is the length of the diagonal of square with perimeter 12 m? Express the answer as a simplified square root.

Answer 1

Answer: $3\sqrt{2}\ m$

Step-by-step explanation:

The perimeter of a square is:

$P=4s$

Where "s" is the lenght of a side of the square.

Then, if the perimeter of this square is 12 m, you can solve for "s" and find its value:

$s=\frac{P}{4}\\\\s=\frac{12\ m}{4}\\\\s=3\ m$

You can calculate the length of the diagonal with this formual:

$d=s\sqrt{2}$

Where "s" is the lenght of a side of the square.

Substituting the value of "s" into the formula  $d=s\sqrt{2}$, you get that the lenght of the diagonal of this square is:

$d=3\sqrt{2}\ m$