This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Form the quadratic equation. Let the width of the rectangular plot be x meters. The length of the plot is 3 meters more than its width, so the length is (x+3) meters. The area of a rectangle is given by the formula: Area = Length × Width. Given that the area is 180 m^2: x(x+3) = 180 Expand the equation: x^2 + 3x = 180 Rearrange into the standard quadratic form ax^2 + bx + c = 0: x^2 + 3x - 180 = 0 This is the quadratic equation representing the situation. Step 2: Solve the equation by factorisation. We need to find two numbers that multiply to -180 and add up to 3. These numbers are 15 and -12. Rewrite the middle term using these numbers: x^2 + 15x - 12x - 180 = 0 Factor by grouping: x(x+15) - 12(x+15) = 0 (x-12)(x+15) = 0 Set each factor to zero to find the possible values for x: x-12 = 0 or x+15 = 0 x = 12 or x = -15 Since x represents the width of the plot, it must be a positive value. Therefore, x = 12 meters. Step 3: Find the dimensions of the plot. Width = x = 12 meters. Length = x+3 = 12+3 = 15 meters. The dimensions of the plot are: Width: 12 m Length: 15 m Send me the next one 📸