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√(2)\ m`

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=(P)/(4)\\\\s=(12\ m)/(4)\\\\s=3\ m`

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

`d=s√(2)`

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

Substituting the value of "s" into the formula
`d=s√(2)`, you get that the lenght of the diagonal of this square is:

`d=3√(2)\ m`