Sides as Expressions
Part of the Triangles section of Coddy's Geometry journey. Lesson 19 of 71.
The sides can all be expressions in one letter. A triangle has sides x, x + 3 and 2x - 1, and its perimeter is 22. Add the sides, set the sum equal to 22 and solve:
Three sides in one letter
x + (x + 3) + (2x - 1) = 22
4x + 2 = 22
x = 5
First collect the like terms. The three x terms make 4x, and the numbers 3 and -1 make 2. Then solve the two-step equation. The question usually asks for the sides as well. With x = 5, the sides are 5, 8 and 9. Substituting back into each expression is part of the answer.
Challenge
A triangle has perimeter 36 and sides x + 2, x + 5 and 2x + 1.
Find 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 Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingHow Short Can It Be?How Long Can It Be?The Range of the Third SideThe FormulaWhole-Number SidesRecap: The Third Side5The Hypotenuse
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeSimplifying the RootRecap: The Hypotenuse8Special Right Triangles
The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 TriangleAll Three SidesWhich Triangle Is It?Recap: Special Triangles11Mixing Area and Pythagoras
Height of an IsoscelesArea from the HeightThe Equilateral TriangleRight Triangle PerimeterRecap: Two Tools3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterEquilateral PerimeterSides as ExpressionsWrite the PerimeterRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg