Answer-
The approximate value of x is 5.7
Solution-
Properties of diagonals of square
- The diagonals of a square bisect each other and meet at 90°
- The diagonals of a square bisect its angles.
- The diagonals of a square are equal.
The converse of 1st property is that if the diagonals meet at right angles, then the quadrilateral must be a rhombus or square. As in this case, each bisected diagonals are of same length, so it must be a square.
From the diagram, applying Pythagoras Theorem,
[tex]\Rightarrow x^2+x^2=8^2[/tex]
[tex]\Rightarrow 2x^2=64[/tex]
[tex]\Rightarrow x^2=32[/tex]
[tex]\Rightarrow x=\sqrt{32}[/tex]
[tex]\Rightarrow x=5.65\approx 5.7[/tex]
Therefore, the approximate value of x is 5.7
