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# PS: ice-cream sign

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Manager
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13 Feb 2007, 08:41
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Pls explain. I am stuck at the point where i need to find the length of the two sides of the triangle.
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Manager
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13 Feb 2007, 08:55
I found the question on another thread. The step to find the base is well explained in the last post on the thread below.

http://www.gmatclub.com/phpbb/viewtopic.php?t=18922

Cheers!
Manager
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13 Feb 2007, 12:28
Sorry I do not understand how to find that base of the triangle. Could someone go through it, I do not see how knowing it iscosoles helps you
Manager
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13 Feb 2007, 13:48
Required is the Perimeter of the 2 sides of the triangle+3/4permeter of the circle.

3/4 Perimeter of the circle = 3/4*2*Pie*2 (radius, r=2)
= 3 Pie

Now to find the sides of the triangle, we should know the base.
To find the base, the attached pic may be helpful. As the radii form a right anbgle at the center, the triangle inside the circle is an isocsles triangle with sides = 2 (radius)

By Pythogoreon Theorem Base = 2* sqrt (2)

We have the base and height (5)

Again by Pythogoreon theorem

Side = sqrt (25 + 2) [Notice that we have to consider 1/2 of the base]
=3sqrt (3)

Hence, total req perimeter = 3+2*3sqrt(3)
= 3+6*sqrt(3) [2 represents for two sides]

Hope this helps.
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ice-cream1.JPG [ 6.41 KiB | Viewed 820 times ]

VP
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13 Feb 2007, 16:31
sgoll wrote:
Required is the Perimeter of the 2 sides of the triangle+3/4permeter of the circle.

3/4 Perimeter of the circle = 3/4*2*Pie*2 (radius, r=2)
= 3 Pie

Now to find the sides of the triangle, we should know the base.
To find the base, the attached pic may be helpful. As the radii form a right anbgle at the center, the triangle inside the circle is an isocsles triangle with sides = 2 (radius)

By Pythogoreon Theorem Base = 2* sqrt (2)

We have the base and height (5)

Again by Pythogoreon theorem

Side = sqrt (25 + 2) [Notice that we have to consider 1/2 of the base]
=3sqrt (3)

Hence, total req perimeter = 3+2*3sqrt(3)
= 3+6*sqrt(3) [2 represents for two sides]

Hope this helps.

Can you please explain how is the triangle a right angled isoceles triangle? Please see the text in red above
Senior Manager
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13 Feb 2007, 18:43
trivikram wrote:
sgoll wrote:
Required is the Perimeter of the 2 sides of the triangle+3/4permeter of the circle.

3/4 Perimeter of the circle = 3/4*2*Pie*2 (radius, r=2)
= 3 Pie

Now to find the sides of the triangle, we should know the base.
To find the base, the attached pic may be helpful. As the radii form a right anbgle at the center, the triangle inside the circle is an isocsles triangle with sides = 2 (radius)

By Pythogoreon Theorem Base = 2* sqrt (2)

We have the base and height (5)

Again by Pythogoreon theorem

Side = sqrt (25 + 2) [Notice that we have to consider 1/2 of the base]
=3sqrt (3)

Hence, total req perimeter = 3+2*3sqrt(3)
= 3+6*sqrt(3) [2 represents for two sides]

Hope this helps.

Can you please explain how is the triangle a right angled isoceles triangle? Please see the text in red above

You know that:
Circumference = 2 x Pi x r

If r is constant, we can conclude that circumference (or length of sector) is proportional to its angle (= 360 degrees).

Therefore; (Length of sector) α (angle of the sector)

S1/S2 = Angle1/Angle2

We can use this knowledge to find any angle if we know the length sector of the circle and we know the length of the circumference.

From the picture, the circumference = 2 x Pi x 2 = 4Pi
and the top sector on the ice cream has length = (3/4) x 4 Pi = 3Pi

The length of the sector under the triangle that you questioned = 4Pi - 3Pi = Pi

Put all info into the equation that I set above.

S1 = Pi
S2 = Circumference of the circle = 4Pi
Angle1 = what we want to know
Angle2 = 360 (Angle of the circumference)

Pi/4Pi = Angle1/360

Angle1 = 360 x 1/4 = 90 degrees

-------------------------------------------------

Or you can use this equation to find the angle of any sector

Length of sector = Angle of the sector x radius

S = @r
Pi = @ x 2
@ = Pi/2

We know that Pi/2 is 90 degrees.
Manager
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13 Feb 2007, 19:22
trivikram wrote:
sgoll wrote:
Required is the Perimeter of the 2 sides of the triangle+3/4permeter of the circle.

3/4 Perimeter of the circle = 3/4*2*Pie*2 (radius, r=2)
= 3 Pie

Now to find the sides of the triangle, we should know the base.
To find the base, the attached pic may be helpful. As the radii form a right anbgle at the center, the triangle inside the circle is an isocsles triangle with sides = 2 (radius)

By Pythogoreon Theorem Base = 2* sqrt (2)

We have the base and height (5)

Again by Pythogoreon theorem

Side = sqrt (25 + 2) [Notice that we have to consider 1/2 of the base]
=3sqrt (3)

Hence, total req perimeter = 3+2*3sqrt(3)
= 3+6*sqrt(3) [2 represents for two sides]

Hope this helps.

Can you please explain how is the triangle a right angled isoceles triangle? Please see the text in red above

It is right angle triangle because the sector is 1/4 of the whole circle therefore 360/4 = 90
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Senior Manager
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13 Feb 2007, 22:36
perimeter of the circular portion is 3*2*pi*2/4

The base of the triangle is sqrt(2)*2

The other sides of the triangle are sqrt(25+2) = 3*sqrt(3)

so perimeter is 6*sqrt(3) + 3*pi

B
13 Feb 2007, 22:36
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