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JH- Geo 2

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JH- Geo 2

by yellowho » Fri Feb 25, 2011 9:49 pm
What is the perimeter of right triangle ABC?

(1) AB = 5
(2) AC = 5root(2)

Given that this is a right triangle and you know 5 and 5root(2). YOu can conclude that this is a 45:45:90 triangle?


I found this discussion that seems to say you can: https://www.beatthegmat.com/geometry-que ... 70340.html
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by Rahul@gurome » Fri Feb 25, 2011 10:23 pm
Solution:
Obviously, each statement alone is not sufficient to answer the question.
We next combine both the statements together and check.
On combining we know that AB is 5 and AC is 5*sqrt2.
Now, in a right angled triangle, hypotenuse is the largest size.
Now since AC > AB, AB can never be the hypotenuse.
So either AC or BC is the hypotenuse.
If AC is the hypotenuse, the BC^2 is {5*sqrt(2)}^2 - 5^2 = 25.
Or BC is 5*sqrt(2).
If BC is the hypotenuse then, BC^2 is 5^2 + {5*sqrt(2)}^2 = 75.
Or BC is 5*sqrt(3).
Since we are getting 2 values of BC, there can be two different values of perimeter.
Or both statements together are not sufficient to answer the question.

The correct answer is (E).
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by yellowho » Fri Feb 25, 2011 10:32 pm
Rahul, Just two follow up questions

1) We know 30/60/90 has lengths x: xroot(3): 2x.
If we know the length of a triangle is x: xroot(3) : 2x do we know if its a 30/60/90?

2) In the previous problem we know two sides of a triangle and one angle. What additional info.will we need to deem that the triangle is a 30-60-90?
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by Rahul@gurome » Fri Feb 25, 2011 10:54 pm
yellowho wrote:Rahul, Just two follow up questions

1) We know 30/60/90 has lengths x: xroot(3): 2x.
If we know the length of a triangle is x: xroot(3) : 2x do we know if its a 30/60/90?

2) In the previous problem we know two sides of a triangle and one angle. What additional info.will we need to deem that the triangle is a 30-60-90?
For 1) Yes. If the sides are in the ratio 1 : sqrt3 : 2 , then it is a 30:60:90 triangle.

For 2) You will need to know exactly which is the right angle, B or A. If B is 90, then it is a 45:45:90 triangle
If A is 90, then the sides are in the ratio 1:sqrt(2) : sqrt(3) .
This is not the ratio required for 30:60:90.
So with the current data, you cannot get a 30:60:90 triangle.
You will need different values of AB and AC in the statements to get 30:60:90 triangle.
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