Answer:
[tex]WX=\sqrt{970}[/tex]
Step-by-step explanation:
The diagonals of a kite intersect at a 90-degree angle. In this figure, right triangle [tex]\triangle WRX[/tex] is formed by half of each of the diagonals.
In any right triangle, the Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.
Segment WR is one leg of the triangle and is given as 21. XR forms the other leg of the triangle, and is exactly half of diagonal XZ. Therefore, [tex]XR=\frac{1}{2}\cdot 46=23[/tex].
The segment we're being asking to find, WX, marks the hypotenuse of the triangle.
Therefore, substitute our known information into the Pythagorean Theorem:
[tex]21^2+23^2=WX^2,\\WX^2=970,\\WX=\boxed{\sqrt{970}}[/tex]
