What is the length of EF⎯⎯⎯⎯⎯?
Triangle ABC is similar to triangle DEF . The length of AC⎯⎯⎯⎯⎯ is 12 cm. The length of BC⎯⎯⎯⎯⎯ is 18 cm. The length of DF⎯⎯⎯⎯⎯ is 10 cm.
c
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Triangle ABC is similar to triangle DEF . The length of AC⎯⎯⎯⎯⎯ is 12 cm. The length of BC⎯⎯⎯⎯⎯ is 18 cm. The length of DF⎯⎯⎯⎯⎯ is 10 cm.
c
Enter your answer in the box.
------ cm
no picture required
PLEASE HELP
1 Answer
Explanation:
If
then
In other words, all pairs of corresponding sides share the same scale factor. As an example, if
When we don't know the scale factor for two similar triangles, we can figure it out by computing the ratio of two corresponding sides. In this question, we know
#(AC)/(DF)=("12 cm")/("10 cm")=6/5.#
Thus,
#(BC)/(EF)=6/5#
And since we know
#("18 cm")/(EF)=6/5#
Cross multiply:
#"18 cm" xx 5 = EF xx 6#
#"90 cm"/6 = EF#
#"15 cm" = EF#
Thus,