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(1)/(4) \ yards=((4*2+1))/(4) =(9)/(4) \ yards`

`A=1(1)/(2) \ yards^(2) =((1*2+1))/(2) =(3)/(2) \ yards^(2)`

In the formula of the area solve for h

`A=W*h\\ \\ h=(A)/(W)`

Substitute the values of W and A

`h=((3)/(2))/((9)/(4)) \\ \\ h=(2)/(3) \ yards`

therefore

the answer is

the height of the banner is
`(2)/(3) \ yards`