In Exercises 21-28, decide whether a triangle can be formed with the given side lengths. If so,

step 1 In this question, we are again asked whether or not a triangle can be formed given the side leng

In Exercises 21-28, decide whether a triangle can be formed...

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Key Concepts

Triangle Inequality Theorem

The Triangle Inequality Theorem is a fundamental principle in geometry that states the sum of the lengths of any two sides of a triangle must exceed the length of the remaining side. This theorem is essential for determining whether a set of three side lengths can form a triangle, as it ensures the sides can connect to enclose a space.

Heron's Formula

Heron's Formula provides a method to calculate the area of a triangle when all three side lengths are known. The formula is especially useful as it does not require knowledge of the triangle's altitude, only requiring the computation of the semi-perimeter first, followed by a specific square root calculation involving the semi-perimeter and each side length.

Semi-perimeter

The semi-perimeter of a triangle is half the sum of its three side lengths and is a critical component in Heron's Formula. It streamlines the area calculation by summarizing the triangle's dimensions into one parameter, making the subsequent computation more efficient.

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