Question

If the length of a diagonal of a square is 20 cm, Find

a) side of the square b) perimeter of the square.​

Answer 1

A square with all sides of length s has a diagonal of length s√2.

That is because the diagonal of the square is the hypotenuse (which is the longest side) of a right triangle with two sides of length s.

The Pythagorean Theorem states:

a2 + b2 = c2

For this square:

s2 + s2 = (20)2

2s2 = (20)2

s2 = (20)2/2

s2 = (20/√2)2

s = 20/√2

s = (√2/√2)(20/√2)

s = (20/2)√2

s = 10√2 cm

Once you do all those calculations, you will realize that a square forms two right triangles with sides of: s, s, s√2

(note: the hypotenuse is s√2).

s√2 = 20

s = 20 / √2

s = 10 √2 cm