Question

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

Answer 1

Answer: C.
`4√(2)` units.

Explanation:

From the given figure , a square is shown with diagonal 8 units.

To find : the length of side (s) of the square .

In a square : All four sides are equal in length and all four angles are right angles.

Thus, The diagonal(hypotenuse) is making two right -angled triangle with the sides of square.

So by Pythagoras theorem of right triangles , we have

`8^2=s^2+s^2\\\\ 64=2s^2\\\\ s^2=(64)/(2)=32\\\\\Rightarrow\ s=√(32)=√(16*2)=4√(2)`

Hence, the length of side s of the square=
`4√(2)` units.

Answer 2

Answer: The correct option is (C)
`4\sqrt2.`

Step-by-step explanation: We are given to find the length of side 's' of the square shown in the figure.

We know that

all the four sides of a square are equal in length and all the four angles are right angles.

So, each of the two equal parts of the square form a right-angled triangle with hypotenuse as the diagonal.

Therefore, using Pythagoras theorem in one of the right-triangles, we get

`s^2+s^2=8^2\\\\\Rightarrow 2s^2=64\\\\\Rightarrow s^2=32\\\\\Rightarrow s=\pm√(32)\\\\\Rightarrow s=\pm4\sqrt2.`

Since the length of a side of a square cannot be negative, so we get

`s=4\sqrt2~\textup{units}.`

Option (C) is CORRECT.