Bunuel wrote:

What is the area of the right triangle shown?

(1) a + b =14

(2) c^2 = a^2 + 36

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To determine the Area, we need to uniquely determine a & b sides of the triangle.

(1) Sum of the sides is known but each side is not.

Insufficient.(2) \(c^2 = a^2 + 36\) on comparing with the Pythagoras theorem for this triangle:\(b^2 = 36\) or \(b = 6\) However, we do not know a.

Insuff(1) + (2) : we know b from (2) and we can find a as (1) gives us the sum of a & b.

Sufficient!Hence

Option (C) is correct.

Best,

Gladi