we know that
the area of the rectangular banner is equal to
[tex] A=W*h [/tex]
where
W is the wide of the banner
h is the height of the banner
in this problem
[tex] W=2\frac{1}{4} \ yards=\frac{(4*2+1)}{4} =\frac{9}{4} \ yards [/tex]
[tex] A=1\frac{1}{2} \ yards^{2} =\frac{(1*2+1)}{2} =\frac{3}{2} \ yards^{2} [/tex]
In the formula of the area solve for h
[tex] A=W*h\\ \\ h=\frac{A}{W} [/tex]
Substitute the values of W and A
[tex] h=\frac{\frac{3}{2}}{\frac{9}{4}} \\ \\ h=\frac{2}{3} \ yards [/tex]
therefore
the answer is
the height of the banner is [tex] \frac{2}{3} \ yards [/tex]
