Results 1 to 3 of 3

Thread: Word problem

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    40

    Word problem

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member pflo's Avatar
    Joined
    Apr 2009
    From
    Albuquerque, NM
    Posts
    157
    Thanks
    7
    Quote Originally Posted by sinjid9 View Post
    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.

    The equation you've got has two variables in it. You need another equation to solve for both variables. Don't forget to draw a picture. What realtionship do AC and CB have to AB?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello sinjid9!

    Did you make a sketch?


    $\displaystyle C$ is a point on line segment $\displaystyle AB$ such that: .$\displaystyle AB\cdot BC \:=\:AC^2$ .[1]

    If $\displaystyle AB$ is 6 cm, find the length of $\displaystyle BC$ to the nearest millimeter.
    Code:
          A           C       B
          *-----------*-------*
          :    6-x    :   x   :

    Let $\displaystyle x \:=\: BC$ . . (Note that: .$\displaystyle 0 \leq x \leq 6$)

    Then: $\displaystyle 6-x \:=\:AC$

    Substitute into [1]: .$\displaystyle 6x \:=\:(6-x)^2 \quad\Rightarrow\quad x^2 - 18x + 36 \:=\:0$

    Quadratic Formula: .$\displaystyle x \;=\; \frac{18 \pm\sqrt{18^2-4\cdot36}}{2(1)} \;=\;\frac{18 \pm6\sqrt{5}}{2} \;=\;9\pm3\sqrt{5}$


    Therefore: .$\displaystyle x \;=\; 3(3-\sqrt{5} \;=\;2.291796068\text{ cm} \;\approx\;\boxed{2.3\text{ mm}}$


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    A geometric interpretation . . .


    Given a line segment $\displaystyle AB$, find an interior point $\displaystyle C$

    Code:
          A           C       B
          *-----------*-------*
          :     x     :   y   :


    so that these two areas are equal.


    Code:
          *-------------------*
          |                   |
        y |                   | y
          |                   |
          *-----------*-------*
          |     x     |   y
          |           |
        x |           |
          |           |
          |           |
          *-----------*
                x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. word problem - the snow plough problem?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Oct 13th 2011, 01:02 PM
  2. Replies: 3
    Last Post: Jan 2nd 2011, 08:20 PM
  3. 1 Word problem and 1 function problem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Apr 21st 2010, 08:01 AM
  4. Replies: 2
    Last Post: Jan 10th 2009, 05:49 AM

Search Tags


/mathhelpforum @mathhelpforum