Question 313097
Let length = x
let width = y
then x x y = 84 -------------- (1)
But width = 9 more than three times length
therefore width = 3x + 9
y = 3x + 9
Substituting in equation (1) we get
x x(3x + 9) = 84
3x^2 + 9x = 84
3x^2 + 9x -84 = 0
Solving the quadratic equation above we get
x =4, x=-7
Ignoring x = -7 (because length cannot be negative)
we get x = 4
then y = 3x + 9 = 12 + 9 = 21.
Length = 4 feet
Width = 21 feet.

Check:
1) Width  = 9 more than 3 times length
= 3 x length + 9
= (3 x 4) + 9
=12 + 9 = 21

2) Area = Length X Width
= 4 x 21 = 84 sq. feet.