Kaitlyn creates an architectural blueprint of a rectangular dining room. the area of the actual dining room is 900 times as large as the area of the dining room on the blueprint. the length of the dining room on the blueprint is 4 inches. what is the length of the actual dining room?

We need to make a scale between blueprint and actual size. The trick in this question is to understand that the scale for the areas and the scale for the lengths are different.
Scale for area is given in the question as
1 unit on blueprint = 900 units in actual.
As the dining room is given to be rectangular we can find the scale for lengths by taking square root of scale for area.

√1 unit on blueprint = √900 units in actual
Therefore, scale for length= 1:30

Thus, by using the scale we can calculate actual length corresponding to 4 inches on blueprint by multiplying 4 with scale
4 inches×1/30=120inches

Answer = 120 inches

5\16 x 2\5 = 10/80simplify to 1/80