Question

You have made a rectangular quilt that is 5 ft by 4 ft. you want to use the remaining 10 square feet of fabric to add a decorative border of uniform width to the quilt. what should the width of the quilt's border be?

Answer 1

The width of the border will be 0.5 ft

Explanation

The length of the rectangular quilt is 5 ft and width is 4 ft.

So, the area of the rectangular quilt $= (length* width)= (5*4)ft^2 = 20 ft^2$

Lets assume, the width of the quilt's border is $x$ ft.

So, the total length of the quilt including the border will be (2x+5) ft and width will be (2x+4) ft

So, the area of the quilt including the border = (2x+5)(2x+4) ft²

As the area of the border is 10 ft² , so the equation will be ...

$(2x+5)(2x+4) - 20 = 10 \\ \\ 4x^2+18x+20 -20 = 10\\ \\ 4x^2 +18x=10\\ \\ 2x^2 +9x= 5\\ \\ 2x^2 +9x-5=0 \\ \\ 2x^2 +10x-x-5=0\\ \\ 2x(x+5)-1(x+5)=0\\ \\ (x+5)(2x-1)=0$

Now applying zero-product property, we will get...

$x+5=0 \\ x=-5$

and

$2x-1=0\\ 2x= 1\\ \\ x= \frac{1}{2} =0.5$

As the width of the border can't be negative, so we will only take x = 0.5 ft

So, the width of the border will be 0.5 ft