Final answer:
Without additional information on the perimeter of triangle MNO or the ratio between the perimeters of triangles MNO and MGH, the exact scale factor k cannot be determined.
Step-by-step explanation:
Finding the Scale Factor in Geometry
To determine the value of the scale factor k when triangle MNO is dilated to create triangle MGH with a known perimeter of 48 units, additional information is required.
Specifically, we need either the perimeter of the original triangle MNO or the perimeters of both triangles to find the exact ratio of dilation, which is the scale factor.
However, with the given information, a definite value for k cannot be calculated.
Scale factors are used to describe the ratio of the dimensions of a dilated figure to the dimensions of the original figure. The perimeter, being a linear measurement, would directly follow this ratio.
Therefore, if the original perimeter were known, the scale factor k could be simply calculated by dividing the perimeter of triangle MGH by the perimeter of triangle MNO.