Final answer:
The application of proportions in similar geometric figures allows us to calculate the length of NM as 6 units, by setting up the equation 5/1 = 30/NM and solving for NM.
Step-by-step explanation:
The question involves finding the length of NM in similar geometric shapes, using the proportionality of corresponding sides. Given that the ratio AB : IJ is 5:1 and the length of FE is 30, we can establish a proportion with NM as the unknown length.
To solve for NM, we create the equation based on proportional sides:
AB / IJ = FE / NM
5 / 1 = 30 / NM
Cross multiplying gives us:
5 * NM = 30
NM = 30 / 5
NM = 6 units
Thus, the length of NM is 6 units, which follows directly from the proportional relationship between the sides of similar geometric figures.
In similar shapes, corresponding sides are proportional. In this case, AB is to IJ as FE is to NM. Since AB : IJ is given as 5:1 and FE is given as 30, we can set up the proportion: AB/IJ = FE/NM. Cross multiplying, 5 * NM = 1 * 30. So, NM = 30/5 = 6. Therefore, the length of NM is 6 units.