Thirty elves would like to build a skating rink, so they can all use it at the same time. santa tells them, they need at least 40 square feet for each skater, so no one will bump into each other. if they build a rectangular rink, what are some possible dimensions (length and width) for the rink?

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

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol

what is the model?

step-by-step explanation: