Question A farmer has a piece of land in the shape of a right-angled triangle OMN, as

Question

Transcribed Image Text:

A farmer has a piece of land in the shape of a right-angled triangle OMN, as shown in the figure below. He allocates a rectangular piece of land PTOR to his daughter, giving her the freedom to choose P anywhere along the boundary MN. Let OM= a, ON = b and P(x; y) be any point on MN. 11.1 11.2 N (0; b) T 0 Determine an equation of MN in terms of a and b. P(x;y) R M(a; 0) Prove that the daughter's land will have a maximum area if she chooses P at the midpoint of MN. A farmer has a piece of land in the shape of a right-angled triangle OMN, as shown in the figure below. He allocates a rectangular piece of land PTOR to his daughter, giving her the freedom to choose P anywhere along the boundary MN. Let OM= a, ON = b and P(x; y) be any point on MN. 11.1 11.2 N (0; b) T 0 Determine an equation of MN in terms of a and b. P(x;y) R M(a; 0) Prove that the daughter's land will have a maximum area if she chooses P at the midpoint of MN.