Answer:
Width of rectangle = 12 feet
Length of rectangle = 25 feet
Step-by-step explanation:
We are given the following information in the question:
Let x be the width of the rectangle.
We are given that:
[tex]\text{Length} = 2\times \text{Width} + 1\\\text{Length} = 2x +1[/tex]
Area of rectangle = 300 square foot
Formula:
[tex]\text{Area of rectangle} = \text{Length}\times \text{Width}[/tex]
Putting the values, we get,
[tex]300 = x\times (2x +1)\\300 =2 x^2 + x\\2x^2 + x -300 = 0[/tex]
We use the quadratic formula to solve this quadratic equation:
[tex]ax^2 + bx + c = 0\\\\x = \displaystyle\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Using the quadratic formula:
[tex]2x^2 + x -300 = 0\\\\x = \displaystyle\frac{-1 \pm \sqrt{1+2400}}{4} = \displaystyle\frac{-1 \pm 49}{4}\\\\x = 12,\frac{-25}{2}[/tex]
Considering the positive value of x
Width of rectangle = 12 feet
Length of rectangle = 2x + 1 = 25 feet
