分别用定长为L的线段围成矩形和圆,那种图形的面积大,为什么?设矩形和为x,则宽为(L-2x)/2,圆半径为L/(2π)S矩形=x*(L-2x)/2=(-2x²+Lx)/2=[-2(x-L/4)²+L²/8]/2≤L²/16S圆形=π[L/(2π)]²=L²/(4
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![分别用定长为L的线段围成矩形和圆,那种图形的面积大,为什么?设矩形和为x,则宽为(L-2x)/2,圆半径为L/(2π)S矩形=x*(L-2x)/2=(-2x²+Lx)/2=[-2(x-L/4)²+L²/8]/2≤L²/16S圆形=π[L/(2π)]²=L²/(4](/uploads/image/z/3641373-45-3.jpg?t=%E5%88%86%E5%88%AB%E7%94%A8%E5%AE%9A%E9%95%BF%E4%B8%BAL%E7%9A%84%E7%BA%BF%E6%AE%B5%E5%9B%B4%E6%88%90%E7%9F%A9%E5%BD%A2%E5%92%8C%E5%9C%86%2C%E9%82%A3%E7%A7%8D%E5%9B%BE%E5%BD%A2%E7%9A%84%E9%9D%A2%E7%A7%AF%E5%A4%A7%2C%E4%B8%BA%E4%BB%80%E4%B9%88%3F%E8%AE%BE%E7%9F%A9%E5%BD%A2%E5%92%8C%E4%B8%BAx%2C%E5%88%99%E5%AE%BD%E4%B8%BA%28L-2x%29%2F2%2C%E5%9C%86%E5%8D%8A%E5%BE%84%E4%B8%BAL%2F%282%CF%80%29S%E7%9F%A9%E5%BD%A2%3Dx%2A%28L-2x%29%2F2%3D%28-2x%26%23178%3B%2BLx%29%2F2%3D%5B-2%28x-L%2F4%29%26%23178%3B%2BL%26%23178%3B%2F8%5D%2F2%E2%89%A4L%26%23178%3B%2F16S%E5%9C%86%E5%BD%A2%3D%CF%80%5BL%2F%282%CF%80%29%5D%26%23178%3B%3DL%26%23178%3B%2F%284)
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