Solve each problem. The perimeter of a triangle is 59 in....

Solve each problem.
The perimeter of a triangle is 59 in. The longest side is 11 in. longer than the medium side, and the medium side is 3 in. more than the shortest side. Find the length of each side of the triangle.

Key Concepts

Linear Equations

Linear equations are mathematical statements of equality involving linear expressions, where each term is either a constant or the product of a constant and a single variable. Solving these equations is fundamental in many algebraic problems, particularly when determining unknown values based on given conditions.

Perimeter Calculation

The concept of perimeter refers to the total distance around a geometric figure. For polygons, and particularly triangles, the perimeter is calculated by summing the lengths of all sides. Understanding this concept is essential when problems provide conditions related to the total length of the sides.

Variable Assignment

Variable assignment involves choosing symbols to represent unknown quantities in a problem. This step is crucial in transforming a real-world problem into a mathematical model, which can then be manipulated and solved using algebraic techniques.

System of Equations

A system of equations is a collection of two or more equations with the same set of unknowns. In the context of word problems, relationships between different parts of the problem are represented as equations that can be solved simultaneously, often using methods such as substitution or elimination.

Algebraic Word Problems

Algebraic word problems involve interpreting real-world situations, extracting relevant information, and translating that information into algebraic expressions and equations. This requires careful reading and understanding of the problem statement to identify relationships between different quantities and set up a system that can be solved mathematically.

Transcript

Please give Ace some feedback