The Pythagorean theorem states:

#a^2 + b^2 = c^2#

Where #a# and #b# are the lengths of the sides of a right triangle and #c# is the length of the hypotenuse of the right triangle.

Susbtituting #color(red)(19)# for #c# and #color(blue)(4a)# for #b# we can solve for #a#:

#a^2 + (color(blue)(4a))^2 = color(red)(19)^2#

#a^2 + 16a^2 = 361

#17a^2 = 361#

#(17a^2)/color(red)(17) = 361/color(red)(17)#

#(color(red)(cancel(color(black)(17)))a^2)/cancel(color(red)(17)) = 21.235

#a^2 = 21.235# rounded to the nearest thousandth.

#sqrt(a^2) = sqrt(21.235)#

#a = 4.608# rounded to the nearest thousandth.

Then we can solve for #b# by substituting #4.608# for #a# in the relationship: #b = 4a#

#b = 4 xx 4.608#

#b = 18.433# rounded to the nearest thousandth.