A farmer wants to make a rectangular plot whose area is60metres squared.the length is2metres more than twice the width.find the length and width

Let w be the width of the rectangular plot in meters.
Let l be the length of the rectangular plot in meters.

The area of a rectangle is given by the formula:
Area = l × w
We are given that the area is 60 m², so:
60 = l × w (Equation 1)

We are also given that the length is 2 meters more than twice the width:
l = 2w + 2 (Equation 2)

Substitute (2w + 2) for l in Equation 1:
60 = (2w + 2) × w

60 = 2w² + 2w
Rearrange the equation to the standard quadratic form (ax² + bx + c = 0):
2w² + 2w - 60 = 0
Divide the entire equation by 2 to simplify:
w² + w - 30 = 0
Factor the quadratic equation. We need two numbers that multiply to -30 and add to 1. These numbers are 6 and -5.
(w + 6)(w - 5) = 0
This gives two possible solutions for w:
w + 6 = 0 ⟹ w = -6
w - 5 = 0 ⟹ w = 5
Since width cannot be negative, we discard w = -6.
So, the width is w = 5 meters.

Substitute w = 5 into Equation 2:
l = 2w + 2
l = 2(5) + 2
l = 10 + 2
l = 12 meters

Area = l × w = 12 m × 5 m = 60 m². This matches the given area.

The length of the plot is 12 meters and the width is 5 meters.