Answer:
32 cm.
Step-by-step explanation:
We first find the length of the sides of the given square using Pythagoras:
16^2 = x^2 + x^2 where x = length of a side.
x^2 = 16^2 / 2 = 128
x = √128.
Now we calculate the length of the square formed by joining the midpoints of the sides of the given square:
The legs of the 4 triangles formed are √128 / 2 cm long and the side of the new square = hypotenuse of a triangle.
So we have, by Pythagoras:
s^2 = 2 * (√128 / 2)^2
s^2 = 2 * 128/4
= 64
So s = 8 cm
and the perimeter = 4*8 = 32 cm.
