A Perimeter Problem
Part of the Fundamentals section of Coddy's Algebra 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 the total of all four sides, which is two lengths plus two widths:
2(x + 3) + 2x = 26
Distribute to get 2x + 6 + 2x = 26. Collect the like terms to get 4x + 6 = 26. Subtract 6 to get 4x = 20, then divide by 4 to get x = 5. The width is 5 cm and the length is 8 cm. Check that 8 + 5 + 8 + 5 = 26.
In a geometry problem, a formula gives you the equation. The formula might be for the perimeter, for the area, or for the angles of a triangle adding to 180°. Write the formula with your expressions in it. The result is an ordinary equation, and you solve it in the usual way.
Challenge
MediumA rectangle is 4 cm longer than it is wide, and its perimeter is 32 cm, so 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