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GRE
GRE Quantitative Reasoning Section

Area of Triangle Compared to a Constant

Very Hard Geometry Triangles

Consider triangle ABC, where the lengths of sides AB, BC, and CA are represented by $a$, $b$, and $c$, respectively. The triangle's area can be computed using Heron's formula, which states that the area $A$ of triangle ABC is given by:

$$ A = ext{sqrt}(s(s - a)(s - b)(s - c)) $$

where $s$ is the semi-perimeter of the triangle, calculated as:

$$ s =\frac{a + b + c}{2} $$

Given that $a = 7$, $b = 8$, and $c = 9$, determine the relationship between the area of triangle ABC (Quantity A) and the value of 36 (Quantity B). What can be concluded about these two quantities?

Hint

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