What is the length of side s of the square shown below?
Accepted Solution
A:
Answer: The correct option is (C) [tex]4\sqrt2.[/tex]Step-by-step explanation: We are given to find the length of side 's' of the square shown in the figure.We know thatall 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[tex]s^2+s^2=8^2\\\\\Rightarrow 2s^2=64\\\\\Rightarrow s^2=32\\\\\Rightarrow s=\pm\sqrt{32}\\\\\Rightarrow s=\pm4\sqrt2.[/tex]Since the length of a side of a square cannot be negative, so we get[tex]s=4\sqrt2~\textup{units}.[/tex]Option (C) is CORRECT.