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Home » Perimeter of Geometric Shapes » Applying the Scale Factor of Similar Triangles to the Perimeter

Applying the Scale Factor of Similar Triangles to the Perimeter

Last updated: Jan 4, 2020 by Ido Sarig · This website generates income via ads and uses cookies · Terms of use · Privacy policy

The scale factor of two similar triangles (or any geometric shape, for that matter) is the ratio between two corresponding sides.

In today's lesson, we will show that this same scale factor also applies to the ratio of the two triangles' perimeter. This is fairly easy to show, so today's lesson will be short.

Problem

Two triangles, ΔABC and ΔADE are similar, ΔABC∼ ΔADE. The scale factor, AB/AD is 6/5. Find the ratio of the perimeters of the two triangles.

Similar triangles in geometry

Strategy

We will use the definition of the scale factor to define one set of sides in terms of the other set of sides, Then, apply the definition of perimeter. and write out the perimeter of both triangles in using one set of sides.

Solution

(1) ΔABC∼ ΔADE //Given
(2) AB/AD = 6/5 //Given
(3) BC/DE = 6/5 //(1), (2), scale factor is the same for all sides in similar triangles.
(4) AC/AE = 6/5 //(1), (2), scale factor is the same for all sides in similar triangles.
(5) AB = 6/5*AD // rearrange (2)
(6) BC = 6/5*DE // rearrange (3)
(7) AC = 6/5*AE // rearrange (4)
(8) PABC=AB+BC+AC //definition of perimeter
(9) PADE=AD+DE+AE //definition of perimeter
(10)PABC=6/5*AD+6/5*DE+ 6/5*AE //(8), (5), (6) , (7), Transitive property of equality
(11)PABC=6/5*(AD+DE+AE) //(10), Distributive property of multiplication
(12) PABC=6/5*PADE //(11), (9), Transitive property of equality
(13) PABC/PADE=6/5

And so we have easily shown that the scale factor of similar triangles is the same for the perimeters.

« A Difficult Geometry Problem With Similar Triangles
Parallel Lines Drawn Through a Point on the Diagonal of a Parallelogram »

About the Author

Ido Sarig is a high-tech executive with a BSc degree in Computer Engineering. His goal is to help you develop a better way to approach and solve geometry problems. You can contact him at [email protected]

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Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

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