Question

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

Answer 1

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

$s^2+s^2=8^2\\\\\Rightarrow 2s^2=64\\\\\Rightarrow s^2=32\\\\\Rightarrow s=\pm\sqrt{32}\\\\\Rightarrow s=\pm4\sqrt2.$

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

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

Option (C) is CORRECT.

Answer 2

Answer: C. $4\sqrt{2}$ units.

Step-by-step 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

$8^2=s^2+s^2\\\\ 64=2s^2\\\\ s^2=\dfrac{64}{2}=32\\\\\Rightarrow\ s=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$

Hence, the length of side s of the square= $4\sqrt{2}$ units.