Geometry

Question Analysis:
This question is about using the properties of congruent right - triangles and the Pythagorean Theorem.
The main focus is on applying the Pythagorean Theorem to find the length of a missing side in a right - triangle, given that two right - triangles are congruent by the HL theorem.

Key Concept Explanation:
The Hypotenuse - Leg (HL) Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, the two right - triangles are congruent.
The Pythagorean Theorem for a right - triangle with legs and and hypotenuse is .

Step - by - Step Solution:
1. In right - triangle , we know the hypotenuse cm and one leg cm. Let the other leg be .
  - According to the Pythagorean Theorem, .
  - Substitute and