the picture in the attached figure
we know that
if ABC is an isosceles triangle
then
AB=BC
angle A=angle C=45 degrees
and
triangle ABD and triangle BDC also are isosceles triangles
AD=BD=x
DC=BD=x
the hypotenuse AC is equal to
[tex] AC=AD+DC\\ AC=x+x\\ AC=2x [/tex]
To find the length AB applying the Pythagorean Theorem
[tex] AC^{2} =AB^{2} +BC^{2} [/tex]
remember that AB=BC
[tex] AC^{2} =2AB^{2} [/tex]
[tex] AC^{2} =2AB^{2}\\\\ AB=\frac{AC}{\sqrt{2}}\\\\ AB=\frac{2x}{\sqrt{2}}\\\\ AB=x\sqrt{2} [/tex]
therefore
the answer is
the length of one leg of the large right triangle in terms of x is equal to [tex] x\sqrt{2} [/tex]
