What is the approximate length of the diagonal of a square if the perimeter of the square is 12 ft?

Question

It must be the approximate length

Answer 1

Squares are equal sided shapes.  The perimeter is 4 times the length of a side.  So each side of the square must be 3 ft in length.  To find the diagonal, we must imagine a line extends from one corner of the square to another.  This forms a triangle with two sides of 3 ft.  The length of the diagonal is the hypotenuse of the triangle, which can be solved using Pythagorean's theorem.  

 

a² + b² = c²

3² + 3² = c²

18 = c²

Square root(18) = C

C = 4.24 ft

Answer 2

If the perimeter of the square is 12ft, then one side must be 12/4 = 3ft.

 

Then, using the pythagorean theorem a² + b² = c², where a and b are the sides and c is the diagonal (hypotenuse),

 

We get:

 

3² + 3² = c² => 9 + 9 = c² => 18 = c² => √18 = c => √9*2 = c => 3√2 = c

 

Approximately then, c = 3 * 1.414 = 4.243