Results 1 to 3 of 3

Math Help - Geometry Word Problem

  1. #1
    Member
    Joined
    Mar 2008
    From
    A forrest
    Posts
    162
    Awards
    1

    Geometry Word Problem

    Okay, so I need some help with these two:

    *8. In the triangle ABC, D and E are the midpoints of AC and BC. The segments AE and BD intersect at F. Show that regions a2 and a4 have equal areas.

    (Picture Below)



    9. A quarter (a 25 cent piece) is 3/4 inch in diameter and when placed 7 feet from the eye will just block out the disc of the moon. If the diameter of the moon is 2160 miles, how far is the moon from the earth?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    615
    Hello, A Beautiful Mind!

    The second one involves similar triangles.


    9. A quarter (a 25-cent piece) is 3/4 inch in diameter and,
    when placed 7 feet from the eye, will just block out the disc of the moon.
    If the diameter of the moon is 2160 miles, how far is the moon from the earth?
    Code:
                  A
      -           *
      :          /|\
      :         / | \
      :        /  |  \
      :       /   |84 \
      d      /    |    \
      :    B*-----+-----*C
      :    /            \
      :   /               \
      :  /                 \
      -D*-------------------*E
        : - - - 2160  - - - :

    The eye is at A.
    The coin is: . BC = \tfrac{3}{4} inch.
    The altitude of \Delta ABC is 84 inches.

    The diameter of the moon is: . DE \:=\:2160 miles.
    The distance to the moon is d miles.

    Since \Delta ABC \sim \Delta ADE, we have: . \frac{d}{2160\text{ miles}} \;=\;\frac{84\text{ inches}}{\frac{3}{4}\text{ inch}}

    Therefore: . d \;=\;\frac{(2160)(64)}{\frac{3}{4}} \;=\;241,\!920 miles.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    In triangle ABC D and E are mid points of AC and BC, Hence DE is parallel to AB.Hence area ADB = area AEB. In that A2 is common. So area A1 = A3. In triangle ABC BD bisects AC. Therefore area ABD = area DBC.Or A1 + A2 = A3 + A4. But A1 = A3. Hence A2 = A4.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A geometry/derivative word problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 14th 2014, 10:45 PM
  2. [SOLVED] Word Geometry Problem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 18th 2009, 11:27 AM
  3. Replies: 2
    Last Post: January 10th 2009, 05:49 AM
  4. Geometry Word Problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 2nd 2007, 08:24 AM
  5. Geometry - word problem
    Posted in the Geometry Forum
    Replies: 14
    Last Post: January 13th 2006, 12:40 PM

Search Tags


/mathhelpforum @mathhelpforum