Question

Amira is painting a rectangular banner 2 1/4 yards wide in the cafeteria. The banner will have a blue background. Amira has enough blue paint to cover 1 1/2 square yards of wall. Find the height of the bannerif Amira uses all of the blue paint. Show your work.

Answer 1

The  height of the bannerif Amira uses all of the blue paint is 2/3. Below is is the solution:

Area = h x w 
1 1/2 = h x 2 1/4
3/2 = h x 9/4 
h = 3/2 / 9/4 
h = 3/2 x 4/9
h = 2/3

Answer 2

we know that

the area of the rectangular banner is equal to

$A=W*h$

where

W is the wide of the banner

h is the height of the banner

in this problem

$W=2\frac{1}{4} \ yards=\frac{(4*2+1)}{4} =\frac{9}{4} \ yards$

$A=1\frac{1}{2} \ yards^{2} =\frac{(1*2+1)}{2} =\frac{3}{2} \ yards^{2}$

In the formula of the area solve for h

$A=W*h\\ \\ h=\frac{A}{W}$

Substitute the values of W and A

$h=\frac{\frac{3}{2}}{\frac{9}{4}} \\ \\ h=\frac{2}{3} \ yards$

therefore

the answer is

the height of the banner is $\frac{2}{3} \ yards$