Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown. What is the greatest possible whole-number length of the unknown side?
O 8 inches
O 9 inches
O 12 inches
O 13 inches

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homozygous. one is homozygous, while two is heterozygous.

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