Question

use the figure to the right to find the length of \\( \overline { u w } \\).

the length of \\( \overline { u w } \\) is \\( \square \\) units.
(type an integer or a decimal.)

the figure is not drawn to scale.

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \( \angle U=\angle V = 90^{\circ}\), \(RZ = VZ\) (given as the two segments from \(R\) to \(Z\) and \(V\) to \(Z\) are equal, assume the triangle - related equal - side property from the figure's symmetry), and \(ZW = ZW\) (common side). By the HL congruence theorem for right - triangles (\(\triangle UZW\cong\triangle VZW\)).

Step2: Use the property of congruent triangles

If \(\triangle UZW\cong\triangle VZW\), then \(UW = VW\). Given \(VW = 47\) (from the side - length marking in the figure).

Answer:

\(47\)