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

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13 Nov 2019, 01:46
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29% (01:20) correct 71% (01:37) wrong based on 55 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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If the base of triangle PQR is 5, what is the perimeter of the triangl  [#permalink]

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13 Nov 2019, 02:10
1
If the base of triangle PQR is 5, what is the perimeter of the triangle?

Let Base = PQ,
(1) The area of triangle PQR is 12.5
--> 1/2*base*height = 12.5
--> 1/2*5*height = 12.5
--> Height = 5
--> Nothing can be said about the length of the other 2 sides --> Insufficient

(2) The length of a side of triangle PQR is 5∗√2
--> Nothing can be said about the length of the other 2 sides --> Insufficient

Combining (1) & (2),

base, PQ = 5, height = 5, one side = 5√2

Two possible cases
Case 1: An isosceles right angled triangle with 45-45-90 angles [PQ = 5, Height = PR = 5 & Hypotenuse, QR = 5√2]
Case 2: An obtuse triangle with base, PQ = 5, PR (obtuse angle = 135 deg) = 5√2, and 3rd side, QR = 5√5
--> Insufficient

IMO Option E
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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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02 Jan 2020, 08:37
1
Why heron's formula is not applicable to this ?
We have area and two sides. Third side can be deduced ?! :O

Kindly guide.
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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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03 Jan 2020, 12:50
ShankSouljaBoi wrote:
Why heron's formula is not applicable to this ?
We have area and two sides. Third side can be deduced ?! :O

Kindly guide.

i too have this doubt
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If the base of triangle PQR is 5, what is the perimeter of the triangl  [#permalink]

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06 Jan 2020, 23:52
Bikramjeet & ShankSouljaBoi

We can have same area with triangles having 2 sides same and only one side different.

For example: both triangles with sides (5,5,6) & (5,5,8) have the same area = 12.

Refer this question also.https://gmatclub.com/forum/what-is-the-area-of-the-triangle-abc-261449.html

ShankSouljaBoi wrote:
Why heron's formula is not applicable to this ?
We have area and two sides. Third side can be deduced ?! :O

Kindly guide.

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

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07 Jan 2020, 07:06
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Bikramjeet ShankSouljaBoi

Heron's formula only goes one way, when you have the three lengths you can find a unique area, not the other way around. It basically states only one unique triangle shape can be made out of three lengths. In our case plugging in the area and two lengths will give two viable solutions for the third length. GMAT will never use this formula however so it's not worth knowing if you're taking the GMAT.
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If the base of triangle PQR is 5, what is the perimeter of the triangl   [#permalink] 07 Jan 2020, 07:06
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