Results 1 to 4 of 4

Math Help - strory problem help

  1. #1
    Junior Member
    Joined
    Nov 2006
    From
    California
    Posts
    36

    strory problem help

    Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed , he discovered that one side was actaully 2 feet longer then he thought and the other was actually 2 feet shorter then he thought. How much less area does he have then he thought he had?

    I was coming up with this anwer 457 ft less then he thought, would that be right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Singular's Avatar
    Joined
    Dec 2006
    From
    Solo, Java
    Posts
    57
    4 feet less?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, fancyface!

    This doesn't require any algebra at all.
    So exactly where is your difficulty?


    Sam lives on a lot that he thought was a square, 157 feet by 157 feet.

    When he had it surveyed, he discovered that
    one side was actaully 2 feet longer then he thought
    and the other was actually 2 feet shorter then he thought.

    How much less area does he have then he thought he had?

    Sam thought he had:  157 \times 157 \:=\:24,649 ft².

    Instead, his lot was actually 159 feet by 155 feet.
    . . So he had: 159 \times 155 \:=\:24,645 ft².

    Let's see, that's a difference of . . . um . . . (Where's my calculator?)

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by fancyface View Post
    Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed , he discovered that one side was actaully 2 feet longer then he thought and the other was actually 2 feet shorter then he thought. How much less area does he have then he thought he had?

    I was coming up with this anwer 457 ft less then he thought, would that be right?
    It depends on where those two sides with errors are on the lot.

    a) If two opposite sides were actually 159 ft each, and so the other two opposites were actually 155 ft each, then,
    He thought the area was (157)(157) = 157^2
    But actual area =
    = (157 +2)(157 -2)
    = 157^2 -2^2
    = (Area of square lot he thought) minus 4.
    Therfore, the actual lot is 4 sq. ft. less than he thought.

    b) If the two sides with errors are adjacent to each other, then the actual lot area can be computed by dividing the actual lot into two triangles. One triangle is an isosceles rigth triangle; the other is a not a right triangle but whose 3 sides are 159, 157 and the hypotenuse of the isosceles right triangle. Not as easy to do. Lots of square roots. Heron's formula.

    c) If the two erroneous sides are opposite each other, then there are two possible ways, depending on which erroneous side is perpendicular to one of the 157-ft side. Again, same method as in part b) above for each way.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum