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Posted by on Tuesday, January 4, 2011 at 7:08pm.

the perimeter of a rectangle is 22 meters, and the perimeter of the triangle is 12 meters. find the dimensions of the rectangle?

  • math - , Tuesday, January 4, 2011 at 7:12pm

    Let l be the length, and w be the width, of the rectangle.

    The perimeter of the rectangle is 2(l+w).

    The perimeter of the triangle is l+w+sqrt(l^2+w^2). sqrt(l^2+w^2) is the hypotenuse of the triangle.

    There are two equations and two variables. Find l and w.

  • math - , Tuesday, January 4, 2011 at 7:16pm

    the hypotneuse is 5 meters so how could i figure the dimensions of the rectangle out?

  • math - , Tuesday, January 4, 2011 at 7:19pm

    The perimeter of the rectangle is 22m. So 2(l+w) = 22.
    l+w = 11
    l = 11-w

    Also, l^2+w^2 = 5^2 by Pythagorean Theorem.

    Substitute in l = 11-w: (11-w)^2+w^2=5^2

  • math - , Tuesday, January 4, 2011 at 7:24pm

    i have the deminsions of the rectangle but i need to know how to get it , the deminsions are 8m by 3m

  • math - , Tuesday, January 4, 2011 at 7:26pm

    Are you referring to the triangle formed by the diagonal of the rectangle and two of its sides? If the dimensions are 8m by 3m, the hypotenuse of said triangle cannot be 5m.

  • math - , Tuesday, January 4, 2011 at 7:29pm

    im referring to the deminsions of a rectangle with a triangle with a hypotneuse of 5m in the top right corner

  • math - , Tuesday, January 4, 2011 at 7:33pm

    Is the base of the triangle the width of the rectangle, and the height of the triangle half the length of the rectangle?

  • math - , Tuesday, January 4, 2011 at 7:35pm

    yes it certainly is

  • math - , Tuesday, January 4, 2011 at 7:37pm

    Ok. Then the perimeter of the triangle is w + l/2 + 5.

    So w+l/2+5 = 12m, and 2(l+w)=22m.

  • math - , Tuesday, January 4, 2011 at 7:41pm

    thank you so very much you are awesome i wish you were my math teacher!

  • math - , Tuesday, January 4, 2011 at 7:45pm

    you are going to end up hating me i am really bad at dimensions so please bear with me.

    a dorm room your sister is considering seems small.the room is rectangular and has a perimeter of 42 feet. the room is 4 feet longer than its width. what are the dimensions of the room?

  • math - , Tuesday, January 4, 2011 at 7:54pm

    Alison -- please post your last question as a separate post.

  • math - , Tuesday, January 4, 2011 at 7:54pm

    nevermind i got it thanks anyway!

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