Final: The Rug, Modeled
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 61 of 63.
A word problem about a rectangle can lead to a quadratic equation. Write the equation first, and solve it later.
The area of a rectangle is width times length. If a rectangle is x meters wide and its length is 2 meters more than its width, the length is x + 2. If its area is 15 square meters, the equation is x(x + 2) = 15. Keep the product of the width and the length as it is. Expanding it is a solving step, not a modeling step. The equation says the same thing as the story, with the width as the unknown.
Challenge
MediumA rug is x meters wide, its length is 3 meters more than its width, and its area is 40 square meters. Write the equation for its area. Keep the product of the width and the length unexpanded.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factoring & Quadratics
1What Factoring Is
Two DirectionsThe Reverse GearUn-Distributing LettersThe Check Is MultiplicationRecap: First Factors4Minus Signs in the Machine
A Negative ProductWhich One Gets the MinusBoth NegativeThe Sign MapRecap: Signs2The Greatest Common Factor
Number and Letter TogetherThe Largest OneHigher PowersThree Terms Share TooRecap: The GCF5Special Shapes
A Missing MiddleThe Shape in LettersThe Perfect SquareThe Minus VersionPrime PolynomialsRecap: Special Shapes3The Sum-Product Machine
Reading the ProductHunting the PairThe Machine in LettersLonger HuntsRecap: The Machine6Factor Completely
Two LayersSquares InsideCompletely Means CompletelyThe Deep CheckRecap: Factor Completely9The Square Root Method
Undoing a SquareArrange, Then RootA Squared PackageRoots That Are Not WholeRecap: Square Roots12Final Challenges
Final: The Full SweepFinal: Factor and SplitFinal: Arrange FirstFinal: The Rug, ModeledFinal: The Rug, SolvedFinal: No Training Wheels