Home > Geometry > Solving Similar Triangles

Suppose you have triangle ABC with AB = 5, BC = 7, and CA = 10, and also triangle EFG with EF = 900, FG = 1260, and GE = 1800. Are these triangles similar, and if so, what is the scale factor?

Answer 1

#DeltaABC# and #DeltaEFG# are similar and scale factor is #1/180#

#color(white)(xx)5/900=7/1260=10/1800=1/180# #=>(AB)/(EF)=(BC)/(FG)=(CA)/(GE)# Therefore #DeltaABC# and #DeltaEFG# are similar and scale factor is #1/180#.

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Answer 2

Sadie Adams

Yes, these triangles are similar. The scale factor between the two triangles can be found by comparing the ratios of corresponding side lengths.

For triangle ABC, the ratio of side lengths AB to EF, BC to FG, and CA to GE are:

AB/EF = 5/900, BC/FG = 7/1260, CA/GE = 10/1800.

Simplifying these ratios, we find:

AB/EF = 1/180, BC/FG = 1/180, CA/GE = 1/180.

Since all corresponding side ratios are equal, the triangles are similar, and the scale factor is 1/180.

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Answer from HIX Tutor

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