|1. maria and 5 of her roommates decide to buy new
furniture for their apartment. macy's is offering 15%
off all full price items. the couch, coffee tables and
two end tables come to $1,250. what is the amount
each roommate needs to pay including the 9% sales
tax?

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

3

step-by-step explanation: