知识点 5
Build a system from a context when two relationships are described.
Use perimeter and area to build a two-equation system for a rectangle.
核心知识
Two unknowns + two relationships = two equations. Translate each sentence describing a relationship into its own equation, then solve the system.
深入理解
Word problems on the SAT describe two quantities connected by two different relationships. Rule: assign variables, write one equation per relationship, then solve.
- Read the problem once to identify the two unknowns.
- Read again to turn each relationship into an equation.
- Use substitution, because the SAT usually gives one simple relationship and one more complicated one.
- Check the answer in context: lengths must be positive, counts must be whole numbers.
Common setups include sum and product, perimeter and area, and cost and quantity.
分步讲解
- Read the problem and identify the two unknown quantities. Assign variables.
- Find the first relationship and write it as an equation.
- Find the second relationship and write it as a separate equation.
- Solve the system using substitution.
- Check that your answer makes sense in context (positive lengths, whole counts, etc.).
常见误解
- Writing only one equation and trying to solve with one variable — two unknowns require two equations.
- Mixing up which quantities go into which relationship (e.g., swapping length and width in a perimeter equation).
- Keeping a negative solution when the context requires a positive value.
题目
示例解析
A rectangle has a perimeter of 28 centimeters and an area of 48 square centimeters. What is the length, in centimeters, of the longer side of the rectangle?
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