Question

What is the length of side s of the square shown below?

Answer 1

length of side s=
`√(2)`

Explanation:

Construction: Name the given figure as ABCD in which AC=2, AD=AB=BC=CD=s.

Solution: Since, ABCD is a square,thus AD=AB=BC=CD=s.

Now, from ΔADC, we get

`(AC)^(2)=(AD)^(2)+(DC)^2`

⇒
`(2)^2=s^2+s^2`

⇒
`4=2s^2`

⇒
`s^2=2`

⇒
`s=√(2)`

Thus, the length of side s=
`√(2)`

Answer 2

The pythagorean theorem states that in a right triangle, a² + b² = c².
Half of the square is a right triangle as it is cut in the image.
The hypotenuse is 2, which is c.
It is a square, so a = b.
Let's say that s is a just for the sake of the equation.
a² + b² = 4.
4 ÷ 2 = a² = 2
Find the square root of a² and 2. 2 is not a square number so it must stay in radical form.
So, the length of s is √2.
Hope this helps!