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Isosceles triangle & Equilateral triangle - Manhattan Gm

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Isosceles triangle & Equilateral triangle - Manhattan Gm

by shanice » Sat Jun 23, 2012 8:07 pm
Hi all,

I have some doubts to clear for the geometry subject:-

As I know, an isosceles triangle have two sides that are equal and are known as 45-45-90 triangle.
Whereas, Equilateral triangle have three equal sides and are known as 30-60-90 triangle.So, they are also known as the right triangle, right?

Since, both the 45-45-90 triangle and 30-60-90 triangle can also be known as the right triangle, how do I know which triangle am I supposed to use for a particular question?

Example question : Given a square with a side of length 5, what is the length of the diagonal of the
square?

I used the 45-45-90 triangle for this question because logically it can be half
of a square and I got the answer right as 5 square root 2.

But what about the below question:-

What is the measure of an edge of a cube with a main diagonal of length square root 60?

Answer is square root 20 (length of the edge of the cube)


How can I know which triangle to apply in this question?

Thank you in advance.
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by gmat_and_me » Sat Jun 23, 2012 8:50 pm
Yes, Isosceles triangle is one where two sides/two angles
are equal. 45-45-90 is one example of an isosceles triangle.
30-30-120 is another.

Any triangle where one angle is 90 degrees is also called
a right triangle.

Equilateral triangle is one where all angles/sides are equal.
So, that means a 60-60-60 split.

You may also do a google search if you want to learn more.

With these data in mind, I think you can proceed to solve the
problems.

HTH
shanice wrote:Hi all,

I have some doubts to clear for the geometry subject:-

As I know, an isosceles triangle have two sides that are equal and are known as 45-45-90 triangle.
Whereas, Equilateral triangle have three equal sides and are known as 30-60-90 triangle.So, they are also known as the right triangle, right?

Since, both the 45-45-90 triangle and 30-60-90 triangle can also be known as the right triangle, how do I know which triangle am I supposed to use for a particular question?

Example question : Given a square with a side of length 5, what is the length of the diagonal of the
square?

I used the 45-45-90 triangle for this question because logically it can be half
of a square and I got the answer right as 5 square root 2.

But what about the below question:-

What is the measure of an edge of a cube with a main diagonal of length square root 60?

Answer is square root 20 (length of the edge of the cube)


How can I know which triangle to apply in this question?

Thank you in advance.
Top
Master | Next Rank: 500 Posts
Posts: 110
Joined: Thu Apr 05, 2012 8:48 am
Thanked: 3 times
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by shanice » Sat Jun 23, 2012 10:00 pm
But how do I use the 45-45-90 triangle or 30-60-90 triangle for this following question?

What is the measure of an edge of a cube with a main diagonal of length square root 60?

Answer is square root 20 (length of the edge of the cube)

I've tried for hours but still can't get the answer.

Please help.
Top
Senior | Next Rank: 100 Posts
Posts: 58
Joined: Sat Mar 05, 2011 9:14 am
Location: Bangalore
Thanked: 20 times
Followed by:5 members
GMAT Score:770

by gmat_and_me » Sat Jun 23, 2012 10:56 pm
I don't have a diagram to explain, but the explanation for the
answer goes like below.

You can also refer to

https://en.wikipedia.org/wiki/Space_diagonal

for the picture. In this picture AC- (ac dash) is the diagonal
of the cube. AC is the diagonal of the face and CC- is the edge.
Angle between all edges is 90degrees as is the angle between the
diagonal of a face and the edge. Hence, you can apply Pythogoras
theorem all around.

To find out the length, you need to find the length of diagonal of
a face.

Diagonal of a cube = rootof(AC^2 + CC-^2). Let CC- be 'a',
the edge of the cube.

Now AC = rootof(a^2 + a^2) = rootof(2) * a

So diagonal of a cube = rootof(2a^2 + a^2) = rootof(3a^2) = root(3)*a
root(60) = root(3) * a
a = root(60/3) = root(20)

HTH
shanice wrote:But how do I use the 45-45-90 triangle or 30-60-90 triangle for this following question?

What is the measure of an edge of a cube with a main diagonal of length square root 60?

Answer is square root 20 (length of the edge of the cube)

I've tried for hours but still can't get the answer.

Please help.
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