Kendra has an unlimited supply of unbreakable sticks of length 2, 4 and 6 inches. Using these sticks, how many non-congruent triangles can she make if each side is made with a whole stick

Unlimited number of triangles.

Step-by-step explanation:

Unlimited number of triangles can be made because Kendra has unlimited supply of unbreakable sticks. If she has limited number of sticks suppose 90 sticks so she can be able to made 30 non-congruent triangles from these number of sticks so if the number is not known so we are unable to say about the number of triangles should be made from unlimited unbreakable sticks.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4