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18 Sep 2018, 22:03
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
31% (01:46) correct
69%
(01:38)
wrong
based on 83
sessions
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Not Attempted Yet
If the base of triangle PQR is 5, what is the perimeter of the triangle?
(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is \(5\sqrt{2}\)
(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is \(5\sqrt{2}\)
19 Sep 2018, 09:12
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Bunuel
IMO, Answer is "C". Please check my explanation and advice.
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IMG_20180919_213840.jpg [ 874.38 KiB | Viewed 2287 times ]
20 Sep 2018, 04:31
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Bunuel
\(?\,\, = \,\,{\text{perim}}\left( {\Delta PQR} \right)\)
Let´s go straight to (1+2) and use the GEOMETRIC BIFURCATION to prove that the correct answer is the official answer (E).
Important:
01. From the question stem and statement (1), we have:
\(\frac{{5 \cdot h}}{2} = 12.5\,\,\,\,\, \Rightarrow \,\,\,h = 5\) (See figure!)
02. Statement (2) was imposed in our (viable!) constructions:
\(R{P_1} = R{P_2} = 5\sqrt 2\)
03. The perimeters of the two triangles constructed are (visually) distinct.
Therefore we presented a viable bifurcation without the need for arithmetic/algebraic calculations!
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
P.S.: although the term "base" is mathematically reserved to isosceles triangles (a base is a side such that the lengths of the other two are equal), it is common to use the term simply as a substitute to the term "side", what was the case here.
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