A recipe calls for 3/4 this is a fraction of a cup of sugar. David has 1/4 also a fraction of a cup. How much more sugar does David need? Simplify your answer.

A. 2/2 fraction c.

B.4/4 also a fraction c.

C. 4/8 fraction c.

D.1/2 also a fraction c.

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