Length = 12 m and width = [tex]\frac{7}{2}[/tex] m.
Solution:
Let the width of the rectangle be w.
Length of the rectangle = 2w + 5
Area of the rectangle given = 42 m²
Area of the rectangle = length × width
length × width = 42
(2w + 5) × w = 42
[tex]2w^2+5w=42[/tex]
Subtract 42 from both sides, we get
[tex]2w^2+5w-42=0[/tex]
Using quadratic formula,
[tex]$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Here, [tex]a=2, b=5, c=-42[/tex]
[tex]$w=\frac{-5 \pm \sqrt{5^{2}-4 \cdot 2(-42)}}{2 \cdot 2}[/tex]
[tex]$w=\frac{-5 \pm \sqrt{25+336}}{4}[/tex]
[tex]$w=\frac{-5 \pm \sqrt{361}}{4}[/tex]
[tex]$w=\frac{-5 \pm19}{4}[/tex]
[tex]$w=\frac{-5+19}{4}, w=\frac{-5-19}{4}[/tex]
[tex]$w=\frac{14}{4}, w=\frac{-24}{4}[/tex]
[tex]$w=\frac{7}{2}, w=-6[/tex]
Dimension cannot be in negative, so neglect w = –6.
Width of the rectangle = [tex]\frac{7}{2}[/tex] m
[tex]$L=2(\frac{7}{2} )+5=12 \ m[/tex]
Hence length = 12 m and width = [tex]\frac{7}{2}[/tex] m.
