Question

The area of a rectangular plot is 36 square meters. The length of the plot (in meters) is one more than twice its width. Find the length and width of the plot.

length (m) ______.
width (m) ______.

Answer 1

The width of the plot is 4 meters and the length is 9 meters.

Step-by-step explanation:

To solve this problem, we can let the width of the plot be x meters. According to the problem, the length of the plot is one more than twice its width, so the length would be 2x + 1 meters. The area of a rectangle is given by the formula A = length * width. So we have the equation (2x + 1) * x = 36. Expanding and rearranging, we get 2x² + x - 36 = 0.

Factoring this quadratic equation, we get (2x + 9)(x - 4) = 0. Setting each factor equal to zero and solving for x, we find x = -4/2 and x = 4. Since the width cannot be negative, we discard x = -4/2 and conclude that the width of the plot is 4 meters. Substituting this value back into the equation for the length, we find the length is 2(4) + 1 = 9 meters.

Answer 2

4m width and 9m length

Step-by-step explanation:

Let the width of the rectangle be x

Length is 1 more than twice width= 1 + 2x

Area of rectangle is L * B

x(2x + 1) = 36

2x^2 + x = 36

2x^2 + x -36 = 0

2x^2 + 9x - 8x -36 = 0

Solving this:

(2x+9)(x - 4) = 0

X = 4 or -4.5

Distance cannot be negative, so x = 4m

The length is thus 2(4) + 1 = 9m