Hi,
An isosceles triangle is a triangle containing two sides of same length & one side of larger length.
Suppose we have a isosceles triangle ABC as depicted in the figure attached.
Here we see that side AB is equal to the side BC
The angle at point A is same as the angle at point C that is almost 45 degrees, Moreover, triangle BDC and ABD are also isosceles.
If: BD=AD=x , then , BD=DC=x
We can see in the figure that AC is equal to AD+ DC
Which means, AC= x+ x= 2x
Now we need to find out the length of AB, here we will use Pythagorean Theorem.
AC^2 = AB^2 + BC^2
Since BC= AB, so we can write it as:
AC^2 = 2AB^2
Taking sq. root on both sides
AC= 2AB
AB= AC/√2
Putting the value of AC as 2x
AB= 2x/√2
Which means AB= x√2
Therefore,the length of one leg of the large right triangle in terms of x will be x√2
Hope it helps!
