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

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
If the base of triangle PQR is 5, what is the perimeter of the triangl  [#permalink]

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18 Sep 2018, 21:03
00:00

Difficulty:

95% (hard)

Question Stats:

28% (01:50) correct 72% (01:35) wrong based on 43 sessions

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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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19 Sep 2018, 08:12
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 $$5\sqrt{2}$$

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GMATH Teacher
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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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20 Sep 2018, 03:31
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, 03:31
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