The triangles are similar by Angle-Angle
The sample size suggested by this statement is 664 option second is correct.
<h3>What is the margin of error(MOE)?</h3>
It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:

Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
At 99% confidence Z = 2.576
By using the MOE formula:
0.05 = 2.376×√(0.5(0.5)/n)
After calculating
n = 663.57 ≈ 664
Thus, the sample size suggested by this statement is 664 option second is correct.
Learn more about the Margin of error here:
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Answer:

Step-by-step explanation:
see the attached figure with the letter D to better understand the problem
we know that
The segment side AD is the height of triangle ABC
so
Triangles PBQ and ABD are similar by AA Similarity Theorem
The area of triangle ABC is equal to

we have

substitute


Remember that
If two triangles are similar then the ratio of its corresponding sides is proportional
so

substitute the given values



5/4 divided by 2 3/8 equals 0.52631578947.