The Scale Factor
Part of the Triangles section of Coddy's Geometry journey. Lesson 52 of 71.
The scale factor is a side of the larger triangle divided by the matching side of the smaller triangle. In the figure, a side of 4 in the small triangle matches a side of 10 in the large one.
Matching sides 4 and 10
Divide the large side by the matching small side:
k = 10/4 = 5/2
Every other side of the large triangle is 5/2 times its matching side in the small triangle. Every angle stays the same.
The scale factor can be a fraction. It is less than 1 when you go from the larger triangle to the smaller one. Going from the side of 10 back to the side of 4, the factor is 4/10 = 2/5. In both directions, the factor is the new side divided by the old side. The two sides must be a matching pair. Matching sides face the same angle in each triangle.
Challenge
Two similar triangles have matching sides 6 and 18.
Find the scale factor k from the small triangle to the large one.
Try it yourself
Solve for k
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 Leg9Similar Triangles
Same Shape, Different SizeThe Scale FactorFinding a SideThe Unknown BelowMatching the CornersRecap: Similar Triangles