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Final: The Fence

Part of the Triangles section of Coddy's Geometry journey. Lesson 68 of 71.

The perimeter of a triangle is the sum of its three sides, even when the sides are written as expressions. Add the three side lengths as they are written, collect the like terms, and solve. If the question asks for the sides, put the value of x back into each expression. In an isosceles triangle the equal side counts twice, and the marks on the figure show which sides are equal. For example, take an isosceles triangle with sides x + 2, x + 2 and x + 5 and perimeter 27. Adding the sides gives 3x + 9 = 27, so x = 6. The sides are then 8, 8 and 11.

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Challenge

A fence of 40 m runs around a triangular garden. Its two equal sides are 2x + 1 and its third side is x + 3.

An isosceles triangle with ticked sides both labelled 2x plus 1 and base x plus 3

Find x.

Try it yourself

(2x + 1) + (2x + 1) + (x + 3) = 40

Solve for x

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This 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 Triangles

4Area

Half the RectangleHeight Is Not a SideRight Triangle AreaFinding the HeightFinding the BaseAny Side Can Be the BaseRecap: Area

7Is It Right?

The ConverseTesting a TriangleAcute or Obtuse?Sorting by the TestRecap: Right or Not

10Scale in the World

ShadowsAcross the RiverA Side with an ExpressionNested TrianglesRecap: Scale in the World

2The 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 Side

5The Hypotenuse

Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeSimplifying the RootRecap: The Hypotenuse

8Special Right Triangles

The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 TriangleAll Three SidesWhich Triangle Is It?Recap: Special Triangles

11Mixing Area and Pythagoras

Height of an IsoscelesArea from the HeightThe Equilateral TriangleRight Triangle PerimeterRecap: Two Tools

3Perimeter

Around the EdgeA Missing SideIsosceles PerimeterEquilateral PerimeterSides as ExpressionsWrite the PerimeterRecap: Around the Edge

6Finding a Leg

Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg

9Similar Triangles

Same Shape, Different SizeThe Scale FactorFinding a SideThe Unknown BelowMatching the CornersRecap: Similar Triangles

12Final Challenges

Final: Three SticksFinal: The FenceFinal: The LadderFinal: The ShadowFinal: Master of Triangles