A new business borrows $320,000 at a yearly simple interest rate of 7%. The total amount the company repays for the loan and interest is $678,400. How long did it
take to pay off the loan?

i think this could be a possible answer (1 / 84) -1

good luck! : d

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