Explain why the method of solving AND the best answer (selected by the asker) to this question are incorrect?
The diagonal of a rectangular field measures 120 ft and the length is 3 ft more than twice the width. Find the length and width of the field.
Answer selected as best by asker:
(d^2) = (L^2) + (w^2) = (120^2)
L = 2W + 3
Substituting
(L^2) + (w^2) = (120^2)
(2w + 3)^2 + w^2 = 120^2
4w^2 + 9 + 12W + w^2 = 14,400
5w^2 + 12w - 14301 = 0
Solving the quadratic equation
w = 52.29 and -54.69
Skipping the negative one
w = 52.29
L = [(2)*(52.29 + 3)] + 3 = 107.58
Checking
d^2 = [(107.58)^2] + [(52.29)^2] = 11,573 + 2,734
d = 119.6
close enough
Note: The correct answers are:
Width = 47.85 ft
Length = 110.05 ft