The height of a curved support beam can be modeled by

152 units

Step-by-step explanation:

height = 19

Width is the difference of roots

-x²/304 + 19 = 0

x²/304 = 19

x² = 19×304

x² = 5776

x = 76, -76

Width = 76 - (-76) = 152 units

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