Stephen does not like yogurt very much, but he loves
apples. since both make a good snack, stephen’s mom
makes a deal with stephen. she will keep the refrigerator
stocked with 5 yogurts, 2 green apples, and 3 red apples
every day. each day, stephen will randomly pick a
snack. use a tree diagram or area model to show all the
possible outcomes in the sample space. what is the
probability stephen will not get three yogurts on three
consecutive days?

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.