Sarah finished two-thirds of her math problems. if she finished 14 problems. how many does she have left to do?

(In the drawing is the work to find the total number of questions)

because there are 21 total questions you'd then subtract

21-14=7

She has 7 questions left to do.

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