MHB Find the scale factor of triangle ABC to triangle DEF

AI Thread Summary
Triangles ABC and DEF are similar, with triangle ABC having a perimeter of 16 cm and triangle DEF having sides of 6 cm, 8 cm, and 10 cm, totaling a perimeter of 24 cm. The scale factor of triangle ABC to triangle DEF is determined to be 2/3 based on the perimeter ratio of 16:24. There is a distinction between the dilation scale factor, which is 3/2, and the scale ratio, which is less than 1 since triangle ABC is smaller. The confusion arises from the terminology used, as the question specifically asks for the "scale factor." Therefore, the correct scale factor from triangle ABC to triangle DEF is 2/3, not 3/2.
masters1
Triangles ABC and DEF are similar.

Triangle ABC has a perimeter of 16cm.

Triangle DEF has side of 6cm, 8cm and 10cm.

What is the scale factor of triangle ABC to triangle DEF?

A. 1/2
B. 1/3
C. 2/3
D. 3/2
E. 2/1

I concluded the answer is D. Am I correct?
 
Mathematics news on Phys.org
What is the scale factor of triangle ABC to triangle DEF?

perimeter of ABC : perimeter of DEF = 16:24 = 2:3
 
There is a difference between the "scale factor of triangle ABC to triangle DEF" and the "scale factor of triangle DEF to triangle ABC". You found the wrong one! Since ABC is smaller than DEF, the scale factor is less than 1.
 
Then, is this textbook example incorrect?
 

Attachments

  • what-is-a-scale-factor-multiplier-similar-triangles.png
    what-is-a-scale-factor-multiplier-similar-triangles.png
    9.1 KB · Views: 130
The dilation scale factor, which is a transformation, of triangle ABC to triangle DEF is 3/2

The scale ratio, like a map's scale, of triangle ABC to triangle DEF is 2/3

Sorry for the confusion.
 
skeeter said:
The dilation scale factor, which is a transformation, of triangle ABC to triangle DEF is 3/2

The scale ratio, like a map's scale, of triangle ABC to triangle DEF is 2/3

Sorry for the confusion.

So, the question asked about "scale factor", not ratio of any kind. Is the answer, in fact, "D", which is 3/2?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top