Finn had 132 boards. He gave 29 boards to his neighbor and stacked all of his remaining boards into piles around his house. Each pile
contained 20 boards. Which equation can be used to find p, the
number of piles of boards Finn made?

Total Boards : 132

Remaining : 29

Each Pile contained : 20

Equation :

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