C is a point on line segment AB such that AB*BC=AC^2. If AB is 6cm, find the length of BC to the nearest millimeter.
I substituted 6 for AB and re-arranged the equation but it didn't do much.
Hello sinjid9!
Did you make a sketch?
is a point on line segment such that: . .[1]
If is 6 cm, find the length of to the nearest millimeter.Code:A C B *-----------*-------* : 6-x : x :
Let . . (Note that: . )
Then:
Substitute into [1]: .
Quadratic Formula: .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
A geometric interpretation . . .
Given a line segment , find an interior point
Code:A C B *-----------*-------* : x : y :
so that these two areas are equal.
Code:*-------------------* | | y | | y | | *-----------*-------* | x | y | | x | | | | | | *-----------* x