Let the width be x.
Then,Length = ( 2x - 3 ) m
According to the question,
Area of rectangle = 665 m² [ Given ]
Formula: Area of rectangle = Length × Width
[tex] \sf \implies \: length \: \times breadth = 665 \: m {}^{2} [/tex]
[tex] \sf\implies \: (2x - 3) \times x = 665[/tex]
[tex] \sf \implies \: 2 {x}^{2} - 3x = 665[/tex]
[tex] \sf \implies \: {2x}^{2} - 3x - 665 = 0[/tex]
By split middle term
[tex] \sf \implies \: 2 {x}^{2} - 38x + 35x - 665 = 0[/tex]
[tex] \sf\implies \: 2x(x - 19) + 35(x - 19) = 0[/tex]
[tex] \sf \implies \: (2x + 35) = 0 \: or \: (x - 19) = 0[/tex]
[tex] \sf \implies \: x = \dfrac{ - 35}{2} \: or \: \: x = 19 \: [/tex]
Note: Ignore negative number.
Now,
Width of a rectangle = 19 m
Length of a rectangle = 2x - 3 = 2 × 19 - 3 = 38 - 3 = 35 m
