Results 1 to 10 of 10

Math Help - Isosceles Triangle Problem

  1. #1
    Newbie Kitty_Kat's Avatar
    Joined
    Apr 2006
    From
    Canada
    Posts
    11

    Question Isosceles Triangle Problem

    Is it possible that on an isosceles triangle if you put squares on the sides, that two of those squares will equal the third?

    ie: If the side lengths were 3,3,5 the squares would be 3x3 , 3x3, and 5x5

    Please help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Kitty_Kat
    Is it possible that on an isosceles triangle if you put squares on the sides, that two of those squares will equal the third?

    ie: If the side lengths were 3,3,5 the squares would be 3x3 , 3x3, and 5x5

    Please help.
    Yes, but you cannot get rational (fraction or whole numbers) length of sides.
    The general form is x,x,x\sqrt{2} for example, 1,1,\sqrt{2}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie Kitty_Kat's Avatar
    Joined
    Apr 2006
    From
    Canada
    Posts
    11

    Exclamation

    Quote Originally Posted by ThePerfectHacker
    Yes, but you cannot get rational (fraction or whole numbers) length of sides.
    The general form is x,x,x\sqrt{2} for example, 1,1,\sqrt{2}

    Do you think it's possible to explain it further? Maybe with pictures because it would help alot. I need to explain it with a picture and prove that this theory is right so any details would help.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Kitty_Kat
    Do you think it's possible to explain it further? Maybe with pictures because it would help alot. I need to explain it with a picture and prove that this theory is right so any details would help.
    I do not know what your math level is but I am going to keep its as simple as possible. You said that when you form squares and the sides and add them you get the square of the third side, thus, in algebraic terms,
    x^2+y^2=z^2- but this is the Pythagorean Theorem. Thus, we must have a right triangle. Now you said that it is isoseles. Thus, two sides are equal. Thus, two of the angles must also be equal. Since one angle is already 90 degrees the other two angles must add up to 90 degrees also because the sum of the angles of ANY triangle is 180. Thus, the other two angles must be 45 and 45. Finally, there is a theorem about a 45-45-90 triangle that says if the smaller sides are x then the biggest side (hypotenuse) is x\sqrt{2}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie Kitty_Kat's Avatar
    Joined
    Apr 2006
    From
    Canada
    Posts
    11

    Arrow

    Quote Originally Posted by ThePerfectHacker
    I do not know what your math level is but I am going to keep its as simple as possible. You said that when you form squares and the sides and add them you get the square of the third side, thus, in algebraic terms,
    x^2+y^2=z^2- but this is the Pythagorean Theorem. Thus, we must have a right triangle. Now you said that it is isoseles. Thus, two sides are equal. Thus, two of the angles must also be equal. Since one angle is already 90 degrees the other two angles must add up to 90 degrees also because the sum of the angles of ANY triangle is 180. Thus, the other two angles must be 45 and 45. Finally, there is a theorem about a 45-45-90 triangle that says if the smaller sides are x then the biggest side (hypotenuse) is x\sqrt{2}

    Well I'm a grade 8 student. I think it's impossible for an isosceles triangle to be part of the pythegorean theorem because if two sides are always the same , as well as angles then wouldn't two of the sides always be equal leaveing the third side on it's own? So I think it's impossible but I need to prove it. The pythegorean Theorem may not work for isosceles triangles.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Kitty_Kat
    Well I'm a grade 8 student. I think it's impossible for an isosceles triangle to be part of the pythegorean theorem because if two sides are always the same , as well as angles then wouldn't two of the sides always be equal leaveing the third side on it's own? So I think it's impossible but I need to prove it. The pythegorean Theorem may not work for isosceles triangles.
    The pythagorean theorem works for any right triangle.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie Kitty_Kat's Avatar
    Joined
    Apr 2006
    From
    Canada
    Posts
    11

    Question

    Quote Originally Posted by ThePerfectHacker
    The pythagorean theorem works for any right triangle.

    Not to be a pest but that means it would work for isosceles triangles as well?
    But how can that be?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Any right isosceles triangle is in the form of x,x,x\sqrt{2} and thus the Pythagorean Thereom holds true. But if it isn't a right triangle then this theorem does not apply.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie Kitty_Kat's Avatar
    Joined
    Apr 2006
    From
    Canada
    Posts
    11

    Post Pythagorean Theorem

    Could you give me a definition of the Pythagorean Theorem to help me with the explanation I'm currently writting?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie Kitty_Kat's Avatar
    Joined
    Apr 2006
    From
    Canada
    Posts
    11

    Smile

    Quote Originally Posted by Jameson
    Any right isosceles triangle is in the form of x,x,x\sqrt{2} and thus the Pythagorean Thereom holds true. But if it isn't a right triangle then this theorem does not apply.

    Thank you, this helps me alot.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Isosceles Triangle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 24th 2011, 01:29 AM
  2. Isosceles right triangle problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 02:12 PM
  3. Replies: 1
    Last Post: September 16th 2009, 01:31 PM
  4. isosceles triangle
    Posted in the Geometry Forum
    Replies: 3
    Last Post: June 5th 2009, 06:07 AM
  5. Replies: 27
    Last Post: April 27th 2008, 11:36 AM

Search Tags


/mathhelpforum @mathhelpforum