Question

Given right triangle A with a hypotenuse length of 2y + x and a leg length of x + y, and right triangle B with a hypotenuse length of 4y + 3 and a leg length of x + 4, for what values of x and y are the triangles congruent by HL?\

Answer 1

2y+x=4y+3 (hypotenuse)
x=2y+3 (1st equation)

x+y=x+4 (leg)
y=4 (2nd equation)

plugging 2nd into 1st equation, 
x=11

so x=11, y=4