In total, we have 3 right triangles.
First, we will use the right-handed triangle, composed of sides 36, x, and y. From this triangle, using Pythagoras we have that y²= 36²+x²
From the left-handed triangle, composed of sides 36, 6x and z, using Pythagoras we have that z² = 36²+36x²
From the big triangle, composed of the sides z, y and 7x, using Pythagoras we have that 49x² = y² + z². We can now replace both y² and z² with the expressions we found before, and after that we will have an equation just with the variable x
49x² = 36² + x² + 36² + 36x²
49x² - x² - 36x² = 36² + 36²
12x² = 2592
x² = 216
x ≅ 14.69
With this value for x we can now replace it on the first 2 expressions we found, and by doing this find the values for y and z
y² = 36² + x²
y² = 1296 + 216
y = √1512
y ≅ 38.88
z² = 36² + 36x²
z² = 1296 + 36(216)
z = √9072
z ≅ 95.24