An interesting right-angled triangle
Level
pending
Triangle ABC is right-angled about B and AC=12. X is the foot of perpendicular from B to AC such that Find the length of BC.
The answer is 6.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Assume BC = x, CX = y.. So AX = y^2. y^2 + y = AX + XC = AC = 12, y^2 + y - 12 = 0, (y + 4)(y - 3) = 0, y = 3. From similarity of triangles AXB, BXC we have BX^2 = AX.XC = y^3. From similarity of triangles BXC, ABC we have x^2 = BC^2 = AC.CX = 12y = 36. Hence BC = x = 6.