Question

A rectangular field with perimeter of 80m is to have an area of at least 380m² . Describe the possible lengths and of the field.​

Answer 1

$let \: x \: be \: the \: length \\ let \: y \: be \: the \: width$

$perimeter = 2x + 2y \\ area = xy$

$2x + 2y = 80 \\ xy = 380 \\ \\ x + y = 40 \\ xy = 380 \\ \\ x = 40 - y \\ (40 - y)y = 380$

$40y - y {}^{2} = 380 \\ y {}^{2} - 40y + 380 = 0 \\ y {}^{2} - 40y + 400 = 20 \\ (y - 20) {}^{2} = 20 \\ y - 20 =± \sqrt{20} \\ y_{1}=20-√20≈15.52786\\ y_{2}=20+√20≈24.4721$