Question

The figure is a square. it's diagonals meet to form four right angles. what is the approximate value of x ?

Answer 1

The answer is 5.7 to your problem

Answer 2

Answer-

The approximate value of x is 5.7

Solution-

Properties of diagonals of square

1. The diagonals of a square bisect each other and meet at 90°
2. The diagonals of a square bisect its angles.
3. 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,

$\Rightarrow x^2+x^2=8^2$

$\Rightarrow 2x^2=64$

$\Rightarrow x^2=32$

$\Rightarrow x=\sqrt{32}$

$\Rightarrow x=5.65\approx 5.7$

Therefore, the approximate value of x is 5.7