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

In the following exercises, solve using the properties of triangles.
One side of a triangle is twice the smallest side. The third side is 5 feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.

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Key Concepts

Triangle Perimeter

The concept of the triangle perimeter involves the sum of the three side lengths of a triangle. When the total perimeter is given, this relationship provides the primary equation that connects the variables representing the side lengths.

Algebraic Representation of Side Relationships

This key concept involves expressing unknown side lengths using variables and algebraic expressions. By assigning a variable to one side and using given relationships (like multiples or additive constants) for the other sides, the problem is translated into algebraic terms.

Solving Linear Equations

Once the relationships among the sides have been established and the perimeter equation is formed, solving the resulting linear equation is essential. This process includes isolating variables, combining like terms, and computing the value of the unknowns.

Triangle Inequality

Although not always explicitly stated, the triangle inequality theorem is an important property of triangles. It states that the sum of any two sides must be greater than the third side, ensuring that the computed side lengths form a valid triangle.

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