In the following exercises, solve using triangle properties....

In the following exercises, solve using triangle properties.
One side of a triangle is three times the shortest side. The third side is three feet more than the shortest side. The perimeter is 13 feet. Find the lengths of all three sides.

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Key Concepts

Perimeter

The perimeter of a triangle is the sum of the lengths of its three sides. It is a common geometric measure used in problems where the total boundary length is known, and it provides a basis for setting up equations relating the sides.

Algebraic Representation of Geometric Relationships

This concept involves using variables to represent unknown side lengths and expressing given relationships among the sides with algebraic equations. It allows the problem solver to convert geometric conditions into a solvable algebraic format.

Solving Linear Equations

In many triangle problems, especially when relationships between side lengths are given, setting up and solving a linear equation is a valuable step. This process involves combining like terms and isolating variables to determine unknown lengths.

Triangle Inequality Theorem

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This principle is crucial in verifying that the computed side lengths indeed form a valid triangle.

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