Triangle abc is similar to triangle def . the length of ac is 10 cm. the length of bc is 15 cm. the length of df is 6 cm.
what is the length of ef?

12

6

10

9

  9 cm

Step-by-step explanation:

Side lengths of similar triangles are proportional. BC is 1.5 times the length of AC, so EF will be 1.5 times the length of DF:

  1.5·6 cm = 9 cm

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the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.