the length of a rectangle is one foot more than twice its width if the area of the rectangle is 300 ft^2 find the dimensions of the rectangle Someone please explain this too me

Answer:Width of rectangle = 12 feetLength 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 footFormula:[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 xWidth of rectangle = 12 feetLength of rectangle = 2x + 1 = 25 feet