GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
An architect is designing a rectangular room. The length (L) of the room is 3 feet more than twice its width (W). If the perimeter of the room is 66 feet, what is the width of the room?
- A12 feet
- B15 feet
- C10 feet
- D8 feet
Show answer & explanationAnswer & explanation
Correct answer: C. 10 feet
From the problem, L = 2W + 3. The formula for the perimeter of a rectangle is P = 2L + 2W. Substitute P=66 and L=2W+3 into the perimeter formula: 66 = 2(2W + 3) + 2W. Simplify: 66 = 4W + 6 + 2W. Combine like terms: 66 = 6W + 6. Subtract 6 from both sides: 60 = 6W. Divide by 6: W = 10 feet.
Why the other options are wrong
- A. Incorrect calculation.
- B. This would be the length if the width was 6 feet, not the correct width.
- D. Incorrect calculation.
Solving Linear Equations (Geometry Applications)
Using geometric formulas (like perimeter or area) and given relationships to set up and solve linear equations for unknown dimensions.
- Write down relevant geometric formulas.
- Express unknown dimensions in terms of a single variable.
- Substitute expressions into the formula and solve the resulting linear equation.
Memory trick: Geometry facts, linear equation acts!