Answer: B
Let the width of the rectangle be \(x\) meters. ∴ The length of the rectangle is \((x + 3)\) meters. ∴ According to the question: \[ \sqrt{x^2 + (x + 3)^2} = 15 \] \[ \sqrt{x^2 + (x^2 + 2 \cdot x \cdot 3 + 3^2)} = 15 \] \[ \sqrt{x^2 + x^2 + 6x + 9} = 15 \] \[ \sqrt{2x^2 + 6x + 9} = 15 \] \[ 2x^2 + 6x + 9 = 15^2 \] \[ 2x^2 + 6x + 9 - 225 = 0 \] \[ 2x^2 + 6x - 216 = 0 \] \[ x^2 + 3x - 108 = 0 \] \[ x^2 + 12x - 9x - 108 = 0 \] \[ x(x + 12) - 9(x + 12) = 0 \] \[ (x + 12)(x - 9) = 0 \] ∴ Either \((x + 12) = 0\) or \((x - 9) = 0\) When \((x + 12) = 0\), then \(x = -12\) [But side length cannot be negative] When \((x - 9) = 0\), then \(x = 9\) ∴ The width of the rectangle is 9 meters and the length is \(9 + 3 = 12\) meters.
Let the width of the rectangle be \(x\) meters. ∴ The length of the rectangle is \((x + 3)\) meters. ∴ According to the question: \[ \sqrt{x^2 + (x + 3)^2} = 15 \] \[ \sqrt{x^2 + (x^2 + 2 \cdot x \cdot 3 + 3^2)} = 15 \] \[ \sqrt{x^2 + x^2 + 6x + 9} = 15 \] \[ \sqrt{2x^2 + 6x + 9} = 15 \] \[ 2x^2 + 6x + 9 = 15^2 \] \[ 2x^2 + 6x + 9 - 225 = 0 \] \[ 2x^2 + 6x - 216 = 0 \] \[ x^2 + 3x - 108 = 0 \] \[ x^2 + 12x - 9x - 108 = 0 \] \[ x(x + 12) - 9(x + 12) = 0 \] \[ (x + 12)(x - 9) = 0 \] ∴ Either \((x + 12) = 0\) or \((x - 9) = 0\) When \((x + 12) = 0\), then \(x = -12\) [But side length cannot be negative] When \((x - 9) = 0\), then \(x = 9\) ∴ The width of the rectangle is 9 meters and the length is \(9 + 3 = 12\) meters.