Results 1 to 4 of 4

Math Help - Isosceles right triangles perp to base...Help.

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    67

    Isosceles right triangles perp to base...Help.

    Base of the solid is the area located by the curve. It says cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. I found the upper limit to be 3 and the lower limit to be -3. Can anyone show me how to find the base and the height? I used the 45/45/90 rule and came up with ((144-16x^2)/9)^(1/2)*((2)^(1/2)/2) for the hypotenuse. I know this is wrong, but now really sure how to actually find the base or height.

    Isosceles right triangles perp to base...Help.-untitled.png

    a=-3
    b=3
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,134
    Thanks
    1013
    Quote Originally Posted by Bracketology View Post
    Base of the solid is the area located by the curve. It says cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. I found the upper limit to be 3 and the lower limit to be -3. Can anyone show me how to find the base and the height? I used the 45/45/90 rule and came up with ((144-16x^2)/9)^(1/2)*((2)^(1/2)/2) for the hypotenuse. I know this is wrong, but now really sure how to actually find the base or height.

    Click image for larger version. 

Name:	Untitled.png 
Views:	34 
Size:	1.5 KB 
ID:	19631

    a=-3
    b=3
    hypotenuse = 2y

    area of a right isosceles triangle is \frac{(hyp)^2}{4} = \frac{(2y)^2}{4} = y^2

    \displaystyle V = 2 \int_0^3 y^2 \, dx<br />

    \displaystyle V = 2 \int_0^3 \frac{144-16x^2}{9} \, dx

    \displaystyle V = \frac{2}{9} \int_0^3 144-16x^2 \, dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2010
    Posts
    67
    Where did the 2y come from? How do you know the hypot. is 2y?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,134
    Thanks
    1013
    Quote Originally Posted by Bracketology View Post
    Where did the 2y come from? How do you know the hypot. is 2y?
    the vertical distance from the x-axis to the elliptical curve is y ... since the ellipse is symmetrical to both axes, the total vertical distance from the lower part of the ellipse to the upper part is 2y.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 1st 2010, 09:37 AM
  2. Are equilateral triangles isosceles?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 11th 2010, 05:12 AM
  3. isosceles triangles help!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 14th 2009, 12:31 AM
  4. figure out isosceles triangles angles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 20th 2007, 10:22 PM
  5. Isosceles Triangles
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: October 5th 2006, 10:38 AM

Search Tags


/mathhelpforum @mathhelpforum