Question

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

Answer 1

Answer:

length of side s=$\sqrt{2}$

Step-by-step 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

$(AC)^{2}=(AD)^{2}+(DC)^2$

⇒$(2)^2=s^2+s^2$

⇒$4=2s^2$

⇒$s^2=2$

⇒$s=\sqrt{2}$

Thus, the length of side s=$\sqrt{2}$

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!