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If the base of triangle PQR is 5, what is the perimeter of the triangl

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If the base of triangle PQR is 5, what is the perimeter of the triangl  [#permalink]

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New post 18 Sep 2018, 22:03
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C
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E

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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 \(5\sqrt{2}\)

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Re: If the base of triangle PQR is 5, what is the perimeter of the triangl  [#permalink]

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New post 19 Sep 2018, 09:12
Bunuel wrote:
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 \(5\sqrt{2}\)



IMO, Answer is "C". Please check my explanation and advice.
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Re: If the base of triangle PQR is 5, what is the perimeter of the triangl  [#permalink]

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New post 20 Sep 2018, 04:31
Bunuel wrote:
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 \(5\sqrt{2}\)

\(?\,\, = \,\,{\text{perim}}\left( {\Delta PQR} \right)\)

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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Re: If the base of triangle PQR is 5, what is the perimeter of the triangl &nbs [#permalink] 20 Sep 2018, 04:31
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