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

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

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10 Oct 2010, 02:01
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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 $$5 * \sqrt 2$$
[Reveal] Spoiler: OA

Last edited by hemanthp on 10 Oct 2010, 02:37, edited 2 times in total.

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

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10 Oct 2010, 02:51
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hemanthp 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)
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

don't forget Kudos if you like this.

(1) This tells us the height of the perpendicular to the side of length 5 is also 5. But given a side and the length of perpendicular to it, you can draw an infinite number of triangles with different side lengths (easy to see if you try to draw). Insufficient !

(2) Length of one of the sides is 5*sqrt(2). Knowing length of 2 sides, you cannot tell the length of the third side. Insufficient

(1+2)Use the two facts together. You now know there is a side of length 5, with perpendiculr 5, and a second side of length 5*sqrt(2). But again 2 triangles possible (one is the obvious right angled one, see figure for the second - the blue side is 5*sqrt(2)). So insufficient

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

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24 Sep 2017, 23:33
If the base of triangle PQR is 5, what is the perimeter of the triangle?
Let QR =5

(1) The area of triangle PQR is 12.5
=> 1/2*QR*height = 12.5
=> height = 5 => perpendicular from P on QR = PX = 5
We don't have details of other sides
Insufficient

(2) The length of a side of triangle PQR is $$5\sqrt{2}$$
so assume PQ = $$5\sqrt{2}$$
We don't have details of 3rd side PR
Insufficient

1+2
As by statement 1 we know PX =5 and by statement 2 we know PQ= $$5\sqrt{2}$$
So by using Pythagoras theorem we can calculate XQ = $$\sqrt{(PQ^2-PX^2)}$$ = 5

So here XQ = 5 => We can mistake here by considering PQR as right triangle, but here we have 2 possibilities.
So here we have two possibility : either X coincides with R, in which case PQR is a right triangle and we can thus find total perimeter. as PR becomes =5
or X lies outside triangle PQR, such that PQR is obtuse triangle and XR =XQ+QR = 10. Here also we can find value of PR using Pythagorean theorem in triangle PXR
=> PR =$$5\sqrt{5}$$.

But in both cases we will get different value of PR and thus different perimeter
Hence insufficient

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Re: If the base of triangle PQR is 5, what is the perimeter of the   [#permalink] 24 Sep 2017, 23:33
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