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So the triangle side lengths (a, b, c) for the first one are (5, 12, 13), respectively.

The perimeter is then P = a + b + c = 5 + 12 + 13 = 30 and the semiperimeter, call it s, is therefore 15.

Using Heron's formula to find the area, \( A = \sqrt{s \cdot (s-a)(s-b)(s-c)} \), we get

\( A = \sqrt{15 \cdot (15-5)(15-12)(15-13)} \)

\( A = \sqrt{15 \cdot (10)(3)(2)} \)

\( A = \sqrt{900} \)

\( A = 30 \)

Nice. I wonder what is the general approach to finding these?

Maybe if we start with P = A, or \(a + b + c = \sqrt{s \cdot (s-a)(s-b)(s-c)}\).

But this is one equation with three unknowns