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
JH- Geo 2
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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).
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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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?
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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For 1) Yes. If the sides are in the ratio 1 : sqrt3 : 2 , then it is a 30:60:90 triangle.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 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.
Rahul Lakhani
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Quant Expert
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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+91-99201 32411 (India)