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

The length of each side of square is 6
`√(2)` inches

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) = (144)/(2\\) } \\`

⇒
`x^(2) = 72`

⇒
`x = √(72)`

⇒
`x = √(36 )` ×
`√(2)`

⇒ x =
`6√(2)`

Hence the length of each side of square in radical form is
`6√(2)` inches