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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
History
Date
Time
Result
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 2309 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.
Attachments
20Set18_3z.gif [ 8.65 KiB | Viewed 2268 times ]
