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

Answer is (e)
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