x = 10.22 in
Solution:
Width of the figure = x in
Length of the figure = (2x + 5) in
Area of the figure = 260 in²
To find the value of x:
Area of the figure = length × width
length × width = 260
(2x + 5) × x = 260
[tex]2x^2+5x=260[/tex]
Subtract 260 from both sides of the equation.
[tex]2x^2+5x-260=0[/tex]
Factor the above quadratic expression.
Quadratic equation formula:
[tex]$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
[tex]$x=\frac{-5 \pm \sqrt{5^{2}-4 \cdot 2(-260)}}{2 \cdot 2}[/tex]
[tex]$x=\frac{-5 \pm \sqrt{2105}}{4}[/tex]
[tex]$x=\frac{-5+\sqrt{2105}}{4}, \ x=\frac{-5-\sqrt{2105}}{4}[/tex]
x = 10.22, x = –12.72006
Dimension of the figure cannot be measured in negative terms.
Hence x = 10.22 in.
