if a rectangle has a length that is nine feet less than three times its width, what is the perimeter of it if its area is 5,670 feet squared

Question

How do i use the quadratic formula in this situation

Answer 1

If L and W are length and width, L=3W-9, WL=5760.

So W(3W-9)=5760; 3W^2-9W-5760=0; W^2-3W-1920=0.

Completing the square: W^2-3W+9/4=1920+9/4; (W-3/2)^2=√1922.25, W-3/2=43.8435 approx.

Therefore W=45.3435 feet and L=127.0304 feet (approx).

Using the quadratic formula W=(3+√(9+7680))/2=45.3435' (the same result as completing the square).

Perimeter=2(L+W)=344.75' approx.