Miss piper randomly selects 3 students to form a party-planning committee for classroom birthdays. if there are 30 people in the class, how many groups can be formed?

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong

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