I) The correct statement is LM² + LN² = MN²
II) MN is called the hypotenuse
III)The length of the diagonal of the square is 8√2 cm.
What is Pythagora's theorem?
From Pythagorean theorem
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Mathematically, it can be expressed as:
c² = a² + b²
c represents the length of the hypotenuse,
a and b represent the lengths of the other two sides.
I)The correct statement is LM² + LN² = MN²
II) MN is called the hypotenuse. This is the side opposite the right angle.
III) Perimeter of square = 4l
where
l is length of side
P = 4l
P = 32 cm
4l = 32
l = 32/4
l = 8 cm
So, each side is 8 cm
AC² = AB² + BC²
Since the diagonal divides the square into 2 right triangles
AC² = 8² + 8²
= 64 + 64
= 128
AC = √128
= 8√2 cm.
The length of the diagonal of the square is 8√2 cm.