In triangle ABC, angle B=90 degrees. Point X is on side AC such that angle BXA=90 degrees., AX=12, CX=4. What is BX?
A
12
X
4
B C
BC^2 - XC^2 = BX^2
AB^2 - AX^2 = BX^2
BC^2 - 4^2 = AB^2 - 12^2
BC^2 = AB^2 - 144 + 16
BC^2 = AB^2 - 128
BC^2 + AB^2 = AC^2
AB^2 -128 + AB^2 = 16^2
2AB^2 - 128 = 256
2AB^2 = 384
AB^2 = 192
AB^2 = AX^2 + BX^2
192 = 144 + BX^2
48 = BX^2
sqrt (48) = BX = 4 sqrt (3)
+32 
