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
This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
ScanSolve AI Answer
Let's solve this problem step-by-step.
Step 1: Define variables.
Let w be the width of the rectangular plot in meters.
Let l be the length of the rectangular plot in meters.
Step 2: Write down the given information as equations.
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)
Step 3: Substitute Equation 2 into Equation 1.
Substitute (2w + 2) for l in Equation 1:
60 = (2w + 2) × w
Step 4: Simplify and solve the quadratic equation for 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.
Step 5: Calculate the length using the value of w.
Substitute w = 5 into Equation 2:
l = 2w + 2
l = 2(5) + 2
l = 10 + 2
l = 12 meters
Step 6: Verify the area.
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.
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