Can the sides of a triangle have lengths 2.4, 6.5, and 7.4?

yes.

Step-by-step explanation:

2.4 + 6.5 = 8.9 (triangle inequality)

8.9 > 7.4

= it is possible to make a triangle wit these measurements.

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