Answer:
Part a) The ratio of the perimeters is 
Part b) The ratio of the areas is 
Step-by-step explanation:
Part A) What is the value of the ratio (new to original) of the perimeters?
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z-----> the scale factor
x-----> the perimeter of the new triangle
y-----> the perimeter of the original triangle

we have

substitute

Part B) What is the value of the ratio (new to original) of the areas?
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z-----> the scale factor
x-----> the area of the new triangle
y-----> the area of the original triangle

we have

substitute


Apply the cosine double angle identity to get:
Cos 2PI/3
Answer: The height of the building is 50.75 feet.
Step-by-step explanation:
The ratio between the height of the object and the casted shadow must be equal for all the objects, as the angle at which the source if light impacts them is the same.
For the person, we know that it is 5.8ft tall, and the shadow is 3.2ft long.
The ratio will be: 5.8ft/3.2ft = 1.8125
Now, if H is the height of the building, and the shadow that the building casts is 28ft, we must have:
H/28ft = 1.8125
Now we can solve this for H.
H = 1.8125*28ft = 50.75 ft
Then the height of the building is 50.75 feet.
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