Rachel L.

asked • 10/01/16

Suppose a triangle has side lengths PQ, QR, and PR, where PR = 2PQ = 3QR. Write the angle measures in order from least to greatest.

 triangle

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Marlene S. answered • 10/01/16

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Rachel,
 
We have triangle PQR
 
The side opposite <P is QR
The side opposite <Q is PR
The side opposite <R is PQ
 
The larger the side, the larger the angle
 
PR is the largest side
QR is the smallest side
PQ is the middle side
 
So the largest angle is Q
The smallest angle is P
The middle angle is R
 
P<R<Q
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David S.

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This one seemed to make sense from a logical standpoint until I looked at it from the algebra point of view.
 
Now I'm questioning whether the shape can really be called a triangle at all!
 
PR is the largest side
QR is 1/3 as long as PR
PQ is 1/2 as long as PR
 
To form a triangle the sum of the two smaller sides must be greater than the largest side, otherwise the figure will not be closed.  If the sum were just equal, it would simply form a line segment.
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10/01/16

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