Results 1 to 5 of 5

Thread: Diagonals of an isosceles trapezium

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    4

    Diagonals of an isosceles trapezium

    There is an isosceles trapezium with both the oblique sides equal to 8 cm, and the parallel sides being 4, and 9 cm respectively.

    It is required to find the diagonals. Now, my answer is 10 cm. Can anyone please verify this ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Basal
    Quote Originally Posted by Basal View Post
    There is an isosceles trapezium with both the oblique sides equal to 8 cm, and the parallel sides being 4, and 9 cm respectively.

    It is required to find the diagonals. Now, my answer is 10 cm. Can anyone please verify this ?
    Not quite. If the height of the trapezium is $\displaystyle h$ cm, then
    $\displaystyle h^2 = 8^2+2.5^2\;*$
    and if the diagonal is of length $\displaystyle d$ cm, then
    $\displaystyle d^2 = h^2 + 6.5^2$
    $\displaystyle =8^2+2.5^2 + 6.5^2$
    $\displaystyle \Rightarrow d = \sqrt{112.5}$
    $\displaystyle =10.61$ cm (2 d.p.)
    Grandad

    * See correction, below!
    Last edited by Grandad; Apr 20th 2010 at 08:01 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by Basal View Post
    There is an isosceles trapezium with both the oblique sides equal to 8 cm, and the parallel sides being 4, and 9 cm respectively.

    It is required to find the diagonals. Now, my answer is 10 cm. Can anyone please verify this ?
    This is correct.

    Note to Grandad: 8cm is not the height, it is the sidelength (or maybe you're just making a mistake I don't understand)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Laurent
    Quote Originally Posted by Laurent View Post
    This is correct.

    Note to Grandad: 8cm is not the height, it is the sidelength (or maybe you're just making a mistake I don't understand)
    You're right - the answer is $\displaystyle 10$ cm, although I don't understand what you mean here. I didn't say the height was $\displaystyle 8$ cm. I had a sign wrong. I should have said
    $\displaystyle h^2 = 8^2 - 2.5^2$
    of course!

    Grandad
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2010
    Posts
    4
    Thanks for verification. I had to be sure because for some reason the textbook gives the answer as sqrt(73), which is clearly wrong.

    Side question : How do you do the root thingy ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Mar 24th 2011, 06:08 AM
  2. Trapezium
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Dec 19th 2010, 12:42 PM
  3. trapezium
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Dec 7th 2009, 02:24 AM
  4. Replies: 4
    Last Post: Feb 9th 2009, 07:36 PM
  5. Area of a trapezium
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: Oct 25th 2007, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum