Find the value of x.

a. first image
b. 5
c. 10
d. second image

This is a right & isosceles triangle A =90° (Given) & AB = BC (given )

Apply Pythagoras

x² = 5(√2)² + 5(√2)² (since the 2 legs are equal)

x² = 5.2 + 5.2 Since (√2)² =2
x²=10 + 10 & x² = 20 & x=√(20) = 2√5 (the answer given are wrong.2√5 is the right answer)

With an isosceles triangle, isosceles means that two of the sides are equal, along with a 90° angle. You already know that one of the equal sides is 5√3. The value of the legs is always the hypotenuse {x}, multiplied by the √2. after doing this very confusing Pythagorean theorem problem, you should end up getting x=5.

P.S.: HopeIhelped... and if I didn't I can explain differently... :)