Let the width be x.
Width = x
Length = 4x + 7
The area is 650 m²
x(4x + 7) = 650
4x² + 7x - 650 = 0
Using quadratic formula:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac} }{2a} [/tex]
a = 4, b = 7, c = -650
[tex]x = \dfrac{-7 \pm \sqrt{7^2 - 4(4)(-650} }{2(4)} [/tex]
[tex]x = 11.9 \ or\ x = -13.7 \text {(rejected, length cannot be negative)}[/tex]
Width = 11.9m
Length = 4(11.9) + 7 = 54.6m
Answer: Length = 54.6m and width = 11.9m
