Question

A small plane is flying a banner in the shape of a rectangle. The area of the banner is 144 square feet. The width of the banner is `1/4` the length of the banner. What are the dimensions of the banner?

Answer 1

Width is 6; Length is 24

Explanation:

Key points:

Rectangle shape

Area `-> 144" " ft^2`

Width = `("length")/4`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let the area be `A = 144`
Let the width be `W`
Let the length be `L`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Known: `A=WxxL=144`...........................(1)

Given: `W=L/4`.............................(2)

`color(blue)("To determine the value of L")`

Substitute (2) into (1) giving

`L/4xxL=144`

`=> L^2/4=144`

Multiply both sides by 4

`4/4 xxL^2=144xx4`

`L^2=576`

Taking the square root of each side

`color(blue)(L=sqrt(576) = 24)`
'~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("To determine the value of W")`

`WxxL=144`

But L=24 so we have

`24W=144`

Divide both sides by 24

`24/24xxW=144/24`

`color(blue)(W=6)`