Question

Amira is painting a rectangular banner 2 3/4 yards wide on a wall 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 length of the banner if Amira uses all of the blue paint.

Answer 1

The length of the banner if Amira uses all of the blue paint is
`(6)/(11) \text { yards. }`

Solution:

Given, Amira is painting a rectangular banner
`2(3)/(4)` yards wide on a wall in the cafeteria.

The banner will have a blue background

Amira has enough blue paint to cover
`1(1)/(2)` square yards of wall.

We have to find the length of the banner if Amira uses all of the blue paint.

Now we know that, area of rectangle = length x width

`\begin{array}{l}{\text { Then, } 1 (1)/(2)=\text { length } * 2 (3)/(4)} \\\\ {(1 * 2+1)/(2)=(2 * 4+3)/(4) * \text { length }} \\\\ {(11)/(4) \text { length }=(3)/(2)} \\\\ {\text { Length }=(3)/(2) * (4)/(11)} \\\\ {\text { Length }=(6)/(11)}\end{array}`

Hence, the length of the rectangle is
`(6)/(11)` yards.