Final answer:
In triangle MNP with a centroid at T, NT can be found by applying the centroid property that divides medians in a 2:1 ratio. NT is 2/3 the length of median NP, which is 90 units long, making NT 60 units.
Step-by-step explanation:
In triangle MNP, if T is the centroid, and given that side NP is 90 units long and the centroid divides the median in the ratio of 2:1, we can find the length of NT. Since PQ is given as 60 units, this appears to be incorrectly mentioned as it's not clear how PQ is related to the triangle. Ignoring the portion about PQ and following the properties of a centroid, we can focus on the median MN (or MP, depending on which one is correct).
To find NT, we should consider that the centroid divides each median into two segments, one twice the length of the other, with the longer segment being adjacent to the vertex. The centroid, therefore, divides the median in a 2:1 ratio from the vertex to the midpoint of the opposite side. If the median is the line segment from vertex M or N to the midpoint of side NP or MP, and knowing NP is 90 units, the entire length of the median would be 90 units. Therefore, NT, which is 2/3 of the median, would be (2/3) * 90, which equals 60 units.