Question

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 1

Let's say the length is L, and the width is W
L is one foot more than 2W, so L=1+2W
the area of the rectangle: A=L*W=300
replace L with 1+2W: (1+2W)*W=300 =>2W^2+W-300=0
solve the quadratic equation: (W-12)(2W+25)=0
W=12 or W=-12.5 (impossible)
so the width is 12, and the length is L=1+2*12=25

please refer to this website for how to factor a quadratic equation
http://www.purplemath.com/modules/factquad.htm

Answer 2

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:

$\text{Length} = 2\times \text{Width} + 1\\\text{Length} = 2x +1$

Area of rectangle = 300 square foot

Formula:

$\text{Area of rectangle} = \text{Length}\times \text{Width}$

Putting the values, we get,

$300 = x\times (2x +1)\\300 =2 x^2 + x\\2x^2 + x -300 = 0$

We use the quadratic formula to solve this quadratic equation:

$ax^2 + bx + c = 0\\\\x = \displaystyle\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using the quadratic formula:

$2x^2 + x -300 = 0\\\\x = \displaystyle\frac{-1 \pm \sqrt{1+2400}}{4} = \displaystyle\frac{-1 \pm 49}{4}\\\\x = 12,\frac{-25}{2}$

Considering the positive value of x

Width of rectangle = 12 feet

Length of rectangle = 2x + 1 = 25 feet