-- All 4 sides of a square are the same length.
The perimeter is 20 cm.
So each side is (20/4) = 5 cm.
-- If you cut the square along its diagonal, and throw one piece away ...
You have a right triangle.
The legs are sides of the square ... 5 cm each.
The hypotenuse is the diagonal of the square, which you have to find.
-- The (hypotenuse of any right triangle)²
= (the length of one leg)² + (the length of the other leg)² .
(Diagonal)² = (5 cm)² + (5 cm)²
(Diagonal)² = (25 cm²) + (25 cm²)
(Diagonal)² = (50 cm²)
Diagonal = √(50 cm²) = 7.07 cm
or 7.1 cm rounded to the nearest tenth.