Diagonal of a square

Question

A square has a diagonal of 24cm. What are its sides? This is on my maths homework and I need the answer. Thanks

Answer 1

Pythagorean theorem

Let s represent the value of the length of any of the sides of the square.

The diagonal of a square forms a triangle with two of the sides.

So, s² + s² = 24²

2s² = 24²

s² = 24²/2

Solve for s.  Only take the positive value for the square root.  And the answer should be in centimeters so put that as part of the answer.

Answer 2

the diagonal of the square forms two isosceles right triangles, two 45-45-90 triangles

in a 45-45-90 right triangle the hypotenuse is always x√2 where x is the length of a side

therefore, 24=x√2

24=x√2

x=24/√2

rationalize the denominator

x=24√2/2

x=12√2 cm is the length of any one of the four sides

if you use the Pythagorean Theorem...

x^2+x^2=24^2

2x^2=576

x^2=288

x=√288

x=√[(144)(2)]

x=12√2 again