A Perimeter Problem
Part of the Fundamentals section of Coddy's Math journey. Lesson 54 of 64.
"A rectangle is 3 cm longer than it is wide, and its perimeter is 26 cm. How wide is it?" Call the width x; then the length is x + 3. The perimeter is all four sides: two lengths and two widths.
2(x + 3) + 2x = 26
Distribute, collect, undo: 2x + 6 + 2x = 26, 4x + 6 = 26, 4x = 20, x = 5. Width 5, length 8, and 8 + 5 + 8 + 5 is 26.
Geometry problems hand you the equation through a formula (perimeter, area, angles of a triangle adding to 180°). Write the formula with your expressions in it, and it becomes an equation of the kind you solve every day.
Challenge
A rectangle 4 cm longer than it is wide has perimeter 32 cm: 2(x + 4) + 2x = 32. Solve for the width x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Fundamentals
1What an Equation Is
The EquationFinding the UnknownThe Same to Both SidesSolved Means AloneRecap: First Equations4Two-Step Equations
Two Layers to UndoSubtract, Then DivideAdd, Then DivideA Division InsideNegatives in Two StepsRecap: Two-Step Equations7Fractions in Equations
A Fraction CoefficientClearing One DenominatorTwo DenominatorsA Fraction Around a SumCross-MultiplyingRecap: Fractions10From Words to Equations
Phrases into ExpressionsSentences into EquationsConsecutive NumbersAge and MoneyA Perimeter ProblemRecap: Words2One-Step Equations
Undoing AdditionUndoing SubtractionUndoing MultiplicationUndoing DivisionInverse OperationsRecap: One-Step Equations5Tidying First
Like TermsTerms and Numbers MixedThe Distributive PropertyDistributing a SubtractionTidy, Then SolveRecap: Tidying First