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 =± √(20) \\ y_(1)=20-√20≈15.52786\\ y_(2)=20+√20≈24.4721`