Final answer:
The student's question involves calculating unknown side lengths of polygons (a triangular field or a quadrilateral plot of land) given the other side lengths or the total perimeter. Methods include using the perimeter for a quadrilateral or vector addition for a triangle, and applying scale factors for drawings.
Step-by-step explanation:
The question pertains to the concept of perimeter in mathematics, more specifically to the calculation of the sides of polygons based on their perimeters or using geometric properties. The student has a triangular field or a four-sided plot of land and needs to calculate unknown side lengths based on the given lengths of the other sides.
In the case of the four-sided plot, if the first three sides A, B, and C are known, the fourth side D can be calculated as the negative sum of the other sides subtracted from the total perimeter. For example, if the perimeter (y) is known and sides A, B, and C are measured, side D can be found using the formula D = y - (A + B + C).
For the triangular piece of land, if two sides are known and represented as displacement vectors, the third side can be found using vector addition. Given sides A and B as vectors, the third side C is the vector that completes the triangle, satisfying the vector equation A + B + C = 0. Therefore, C can be calculated as C = - (A + B).
An example with a scale factor involves converting real measurements to a drawing. If the longest side of a triangular flower bed is 5.5 meters and the scale is 1/20, then the length of this side in the drawing is 5.5 / 20 = 0.275 meters.