To solve the problem we must know about isosceles right triangle and the Pythagorean Theorem.
A triangle with two sides of equal length and the corresponding angles of equal measurement is known as Isosceles Triangle.
A tringle with a 90° angle is known as a right-angled triangle.
The length of one leg of the large right triangle in terms of x is x√2.
Given to us
As it is given to us that the triangle is a right angle triangle the two sides of the triangle will be equal to each other.
therefore, AB = BC
Also, given that the altitude of the triangle is equal to x. therefore,
AB = x
AB = BC = x,
We know that in a right-angled triangle the longest side of the triangle is the hypotenuse, which is always opposite to the 90° angle.
AC is the hypotenuse,
Using Pythagoras theorem,
AC² = AB² + BC²
[tex]AC^2 = {x^2 + x^2}\\\\ AC = \sqrt{x^2 + x^2}\\\\ AC = \sqrt{2x^2 }\\\\ AC = x\sqrt{2 }\\[/tex]
thus, the value of hypotenuse is x√2.
Hence, the length of one leg of the large right triangle in terms of x is x√2.
Learn more about Hypotenuse:
https://brainly.com/question/8587612
