The altitude is the mean proportional between the left and right parts of the hyptenuse
#13
12/z = z/3
z² = 36
z = 6
By the Pythagorean theorem:
x = √(12²+6²) = √(144+36) = √180 = 6√5
y = √(3²+6²) = √(9+36) = √45 = 3√5
The answers are x=6√5, y=3√5, z=6
#14
2/y = y/6
y² = 12
y = √12 = 2√3
By the Pythagorean theorem:
x = √((√12)²+6²) = √(12+36) = √48 = 4√3
The answers are x=4√3, y=2√3