Question

The diagonal of a square is 12 inches long. What is the length, in inches, of each side of the square? Write the answer in simplified radical form

Answer 1

Answer:

The length of each side of square is 6$\sqrt{2}$ inches

Step-by-step explanation:

Since the diagonal of square is 12 inches.

Let the side of the square in x inches.

As all the angles in square are right angles.

So Using the Pythagoras theorem , we can say that

$x^{2} + x^{2} = 12^{2}$

⇒ $2x^{2} = 144$

⇒ $x^{2} = \frac{144}{2\\} }$

⇒ $x^{2} = 72$

⇒$x = \sqrt{72}$

⇒ $x = \sqrt{36 }$ ×$\sqrt{2}$

⇒ x =$6\sqrt{2}$

Hence the length of each side of square in radical form is $6\sqrt{2}$ inches