To solve this problem, we need to identify the relationship between the altitude and the legs of an isosceles right triangle.
1. Properties of the triangle:
- An isosceles right triangle has two sides of equal length, and the angles opposite these sides are both 45 degrees.
- The hypotenuse is the side opposite the right angle, and it's longer than either of the legs.
2. Altitude in an isosceles right triangle:
- The altitude of an isosceles right triangle, when dropped from the right angle to the hypotenuse, bisects the hypotenuse into two equal segments and also forms two smaller 45-45-90 right triangles within the larger one.
3. Length relationships in a 45-45-90 triangle:
- In a 45-45-90 triangle, the hypotenuse is [tex]\( x \sqrt{2} \)[/tex] times as long as each leg. Therefore, if the legs have length [tex]\( a \)[/tex], then the hypotenuse has length [tex]\( a \sqrt{2} \)[/tex].
4. Using the given altitude:
- The altitude, [tex]\( x \)[/tex], of the large isosceles right triangle bisects the hypotenuse into two equal segments, each of [tex]\( \frac{hypotenuse}{2} \)[/tex]. Hence, the formula linking the hypotenuse to the legs applies equally.
Combining these properties, we recognize that in any isosceles right triangle, with an altitude equal to [tex]\( x \)[/tex]:
- If we let the legs of the large isosceles right triangle be [tex]\( a \)[/tex] units long, the relationship in a 45-45-90 triangle tells us that the length of one leg is indeed simply [tex]\( x \)[/tex].
Putting this all together, the length of one leg of the large right triangle is [tex]\( x \)[/tex] units.
So, the correct answer is:
[tex]\[ x \, units \][/tex]
