The perimeter of a triangle is 5 times the length of the...

The perimeter of a triangle is 5 times the length of the shortest side. The length of the longer side is $9 \mathrm{~cm}$ longer than the length of the shortest side. The length of the middle side is $4 \mathrm{~cm}$ less than the length of the longest side. Find the lengths of the sides.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solving Linear Equations

Once equations have been established, the process of solving linear equations involves techniques such as combining like terms, isolating variables, and applying inverse operations. This fundamental algebraic method is critical for finding numerical values that satisfy the given relationships in a problem.

Triangle Perimeter

The concept of a triangle's perimeter is based on the geometric idea that it is the sum of the lengths of all its sides. Recognizing how individual side lengths contribute to the overall perimeter is essential when problems provide a condition linking the perimeter to one or more of the sides.

Algebraic Modeling

This involves translating real-world or verbal descriptions into algebraic expressions and equations. By representing unknown quantities with variables and expressing their relationships algebraically, one can systematically approach and solve problems involving geometric figures or other contexts.

Setting Up Equations

This key concept is about utilizing the given relationships and conditions to form mathematical equations. In many problems, especially involving proportions or differences between quantities, careful interpretation of the text allows for the creation of equations that capture the constraints imposed on the unknowns.

Transcript

Please give Ace some feedback