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# triangles

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A triangle has integer side lengths 2, 5 and x. What is the area of the triangle if x = 6?

Jul 11, 2022

You can use the formula $$A = \sqrt{s(s-a)(s-b)(s-c)}$$ to solve this. The variable represents the semiperimeter which is: 2 + 5 + 6 = 13 , half of that is 7.5.
$$A = \sqrt{7.5(7.5-2)(7.5-5)(7.5-6)} = \sqrt{7.5\times20.625} = \sqrt{154.6875} = \boxed{\frac{15}{4}\sqrt{11}}$$