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. Send me the next one 📸