Mr. kent is making prize bags for a fundraiser using two types of items. he has mini pencils, mini pens, and mini puzzles that he can choose from to make these prize bags. whichever two items he chooses, he wants to put in each bag the same number of the first item and the same number of the second item, so that all of the items of each type will be used. looking at the pairings below, determine what is the maximum number of bags that mr. kent will make with those items.

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.