Write an equation Josie can use to find the required width of the border, x.

Question

Josie knit a rectangular scarf that measures 6 feet by 1 foot. She wants to use
the remaining 4 square feet of fabric to create a border around the scarf.
Write an equation Josie can use to find the required width of the border, x.

Answer 1

The answer is that the width of the border must be   Width=(-7)/4+(√65)/4

 

To get this you must imagine the scarf with an area of length x width = 6' * 1'

And then imagine the scarf with a border, x having an area of (6 + 2x) * (1+2x)

 

If you calculate the area of the scarf with a border and subtract the area of the scarf without

the border, the answer has to be 4' square, because that's how much material you have.

 

It works out to this:  4x² + 14x + 6 - 6 = 4  which =  4x² + 14x - 4 = 0

Using the quadratic equation gives us a value for the border of (-7)/4+(√65)/4

 

You can test the number and when bordering the scarf, the area = 4 square ft.