GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsEasy
A carpenter is building a rectangular frame. The length of the frame is 5 feet more than its width. If the area of the frame is 84 square feet, which equation can be used to find the width (w) of the frame?
- Aw(w + 5) = 84
- Bw^2 + 5 = 84
- C2w + 2(w + 5) = 84
- Dw + 5w = 84
Show answer & explanationAnswer & explanation
Correct answer: A. w(w + 5) = 84
The area of a rectangle is calculated by multiplying its length by its width. By expressing the length in terms of the width, we can set up a quadratic equation to solve for the width.
Why the other options are wrong
- B. This equation incorrectly represents the length as 'w^2' and does not correctly multiply length by width.
- C. This equation represents the perimeter, not the area, of the rectangle.
- D. This equation incorrectly represents the area and would lead to a linear, not quadratic, solution.
Quadratic Equations from Word Problems (Area)
Word problems involving the area of geometric shapes (especially rectangles) where one dimension is expressed in terms of another often lead to quadratic equations.
- Area of a rectangle = length × width.
- Define variables carefully based on the relationships given.
- The resulting equation can usually be solved by factoring, using the quadratic formula, or completing the square.
Memory trick: Dimensions Dictate the Equation.