Solve using a geometry formula. One side of a triangle is...

Solve using a geometry formula.
One side of a triangle is twice the smallest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.

Key Concepts

Translating Word Problems to Equations

This concept involves interpreting the given information in a problem and converting it into algebraic equations. It requires understanding the relationships described in words, representing unknowns with variables, and systematically setting up equations that reflect conditions such as proportional relationships or fixed differences in measurements.

Linear Equation Solving

Solving linear equations entails performing algebraic operations such as combining like terms and isolating the variable to find its value. This is a key skill in determining unknown side lengths when the relationships between them and the total perimeter are expressed as a linear equation.

Triangle Perimeter

The perimeter of a triangle is the total distance around it, calculated by the sum of its three side lengths. This concept is fundamental when a problem provides relationships between the sides and a specific value for the perimeter, allowing one to set up an equation that represents the cumulative length of the sides.

Algebraic Representation

Algebraic representation involves assigning variables to unknown quantities and expressing relationships between those variables using equations. In geometric problems, especially those dealing with side lengths of figures like triangles, this technique simplifies the analysis by translating verbal descriptions into mathematical expressions that can be manipulated.

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