Explanation:
it is a rectangle.
the area is a rectangle is
length × width
in our case
length × width = 55 ft²
length = 3×width + 4
we use that in the first equation :
(3×width + 4)×width = 55
3×width² + 4×width - 55 = 0
the general solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
so,
width = (-4 ± sqrt(4² - 4×3×-55))/(2×3) =
= (-4 ± sqrt(16 + 660))/6 = (-4 ± sqrt(676))/6 =
= (-4 ± 26))/6
width1 = (-4 + 26)/6 = 22/6 = 11/3 = 3 2/3 ft
width2 = (-4 - 26)/6 = -30/6 = -5
negative numbers for the size of a physical object don't make sense, so
11/3 = 3 2/3 ft is our solution.
length = 3×width + 4 = 3×11/3 + 4 = 11 + 4 = 15 ft
so,
the length = 15 ft
the width = 3 2/3 ft (or 11/3 ft)