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PS - Icecream

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Priti
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PS - Icecream [#permalink] New post   Updated on: 15 Aug 2005, 13:27
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A
B
C
D
E

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Hi,

This Q involves a fig...dont' know how to draw it here but will try to explain...

A circle of radius 2 lies on a triangle is such a way that only 3/4 of its circumference is outside the triangle. The height of the triangle is 5 feet. What is the outer perimeter in feet of this figure? This is an isoceles triangle.

1. 3pi + 3sqrt(3)
2. 3pi + 6sqrt(3)
3. 3pi + 2sqrt(33)
4. 4pi + 3sqrt(3)
5. 4pi + 6sqrt(3)

Thanks.[/img]

I've tried attaching the figure here, AC is the height = 5 feet of he isoceles triangle.



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Originally posted by Priti on 15 Aug 2005, 08:17.
Last edited by Priti on 15 Aug 2005, 13:27, edited 1 time in total.
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Re: PS - Icecream [#permalink] New post   15 Aug 2005, 11:15
I am taking a guess on this; 2 should be the answer;

I cannot visualize the fig; but if 75% of circle is outside the triangle then perimeter of circle = 3/4*2*pi*2=3pi

and height of triangle is 5 and if the triangle covers half circle then
identical sides = sqrt(29) i.e. 5^2+2^2.

but 75% of circle is outside the triangle; so the base will 75% of 4 = 3 or ~=2sqrt2

identical sides = sqrt (25+2) = 3sqrt (3)

so perimeter = 3pi+2(identical sides of the triangle)

no sure if my explanation is clear;
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Re: PS - Icecream [#permalink] New post   24 Sep 2005, 13:36
1/4 angle is 90 degrees.

that gives base of triangle as 4*root2.

that gives side as - root33

outer perimeter is 3pi + 2root33

B
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Re: PS - Icecream [#permalink] New post   24 Sep 2005, 17:22
2. both radii form a 45-45-90 triangle. the hypotnuse becomes the chord (base of the cone) which divided by 2 gives us the length necessary to solve for each side of the isoceles triangle.
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Re: PS - Icecream [#permalink] New post   26 Sep 2005, 11:05
I get B too...only profound rule is the height of the triangle divides the base equally....
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Re: PS - Icecream [#permalink] New post   26 Sep 2005, 11:15
Can someone draw the diagram and show ... i am still confused and couldnt understand the solution..
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Re: PS - Icecream [#permalink] New post   26 Sep 2005, 21:41
Yeah finally figured it out...

I am attaching a diagram if it helps....


3/4rth the circumference of the circle = 3/4*(4*pi) = 3pi

Similarly from the figure, the total base = 2sqrt(2)
Since they are isoceles triangles, each of the sides are 3sqrt(3)

So total perimeter = 3pi + 6sqrt(3)
B for me too...
Attachments

triangle.JPG
triangle.JPG [ 6.27 KiB | Viewed 1708 times ]

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Re: PS - Icecream [#permalink] New post   29 May 2007, 01:19
i'm still confused.

The circumference of the circle is defined as 3/4. Given the radius of 2 and C=pi2r we get a total circumference of C=4pi.

3/4 * 4pi = 3pi

How do we do calculate the base with a height of 5?



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Re: PS - Icecream [#permalink]
29 May 2007, 01:19
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