taneja.niks wrote:What is the perimeter of the triangle?

1. hypotenuse is equal to 5
2. area of triangle = 6

The wording of this question doesn't really make sense. We do not know in advance that the triangle is a right triangle, so it's odd that Statement 1 mentions a 'hypotenuse'. I suppose the question designer intends for Statement 1 to tell us two things: we have a right triangle, and the longest side is 5. That's not sufficient; the sides might be 3-4-5, or they might be 1-sqrt(24)-5, among other possibilities. Statement 2 is clearly not sufficient alone; we might have a 3-4-5 triangle, or we could have a triangle with a base of 12,000 and a height of 1/1000, say, which will have a very large perimeter.

Together, we have three sides of a right triangle, a, b and 5, where:

ab = 12 (from the area)
a^2 + b^2 = 25 (Pythagorean Theorem)

There are quite a few ways to proceed here, but it does happen often enough that you get information about a^2 + b^2 and about ab in the same question. You might then notice that you can use the relationship (a+b)^2 = a^2 + b^2 + 2ab. Doing that here, using substitution:

(a+b)^2 = a^2 + b^2 + 2ab
(a+b)^2 = 25 + 2(12)
(a+b)^2 = 49
a + b = 7

(we ignore the negative solution in the last line here, since a and b are lengths and cannot be negative). So a+b = 7 and the perimeter, a+b+5, is equal to 12. So the answer is C.