Answer:
D
Step-by-step explanation:
We name the corners of the triangle as the attached image.
As we can see, triangle ABC is a right-angled triangle with Angle B equal to 90 degree.
As ABC is a right triangle, so that total measures of angle A and angle C is 90 degree
=> m∠A + m∠C = 90
=> m∠A + 45 = 90
=> m∠A = 90 - 45 = 45
=> m∠A = m∠C
So that ABC is also an isosceles triangle.
=> AB = AC = x
As ABC is a right triangle, according to Pythagoras theorem, we have the following equation:
AB^2 + BC^2 = AC^2
=> x^2 + x^2 = 20^2
=> 2.x^2 = 400
=> x^2 = 400/2 = 200
=> x = [tex]10\sqrt{2}[/tex] ≈ 14.14
So that x ≈ 14.14, the correct answer is D
