Let's solve this problem step-by-step by analyzing the properties of an isosceles right triangle.
1. Understanding the isosceles right triangle:
- An isosceles right triangle has two equal legs and one right angle (90 degrees).
- The two equal legs meet at the right angle.
- The hypotenuse is opposite the right angle.
2. Altitude of the isosceles right triangle:
- The altitude in this triangle is drawn from the right angle to the hypotenuse.
- The altitude also splits the isosceles right triangle into two smaller, congruent right triangles.
- The altitude, in this case, is given as [tex]\( x \)[/tex] units.
3. Properties of the smaller right triangles:
- Each of these smaller triangles is a 45-45-90 triangle.
- In a 45-45-90 triangle, the legs are congruent, and the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.
4. Finding the length of one leg:
- The altitude ([tex]\( x \)[/tex] units) of the original triangle is the leg of one of the smaller 45-45-90 triangles.
- Since the altitude splits the original isosceles right triangle into two congruent smaller 45-45-90 triangles, the hypotenuse of these smaller triangles is the same as the legs of the original triangle.
5. Hypotenuse calculation:
- The length of the hypotenuse (which is also the leg of the original isosceles right triangle) is:
[tex]\[
\text{Hypotenuse} = x \sqrt{2}
\][/tex]
Therefore, the length of one leg of the original isosceles right triangle in terms of [tex]\( x \)[/tex] is [tex]\( x \sqrt{2} \)[/tex] units.
The correct answer is [tex]\( x \sqrt{2} \)[/tex] units.
