A triangular lot ABC has a bearing and distance of line AB to be N 40deg E and 800m and CA equal to 960m long. The lot is to be divided such that the area of APO is only 4 of the area of ABC. Point O is along the line AB and point P is along the line CA. Compute the distance AO and the dividing line PO. The area of triangle ABC is 300, 000 sq. m. AP is equal to 600m long.

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.