Question

1. a 35 - foot wire is secured from the top of a flagpole to a stake in the ground. if the stake is 14 feet from the base of the flagpole, how tall is the flagpole?
2. if the diagonal of a square is 11.3 meters, approximately what is the perimeter of the square?

Explanation:

Step1: Use Pythagorean theorem for problem 9

Let the height of the flagpole be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 35\) (the length of the wire) and \(a=14\) (the distance from the base of the flagpole to the stake). So \(h^{2}+14^{2}=35^{2}\), which can be rewritten as \(h^{2}=35^{2}-14^{2}\).

Step2: Calculate \(h^{2}\)

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Step3: Find \(h\)

\(h=\sqrt{1029}\approx32\) (rounded to the nearest whole number)

Step4: Use diagonal - side relationship for problem 10

For a square with side length \(s\), the diagonal \(d\) is related by \(d = s\sqrt{2}\). Given \(d = 11.3\), then \(s=\frac{d}{\sqrt{2}}=\frac{11.3}{\sqrt{2}}\approx\frac{11.3}{1.414}\approx8\)

Step5: Calculate the perimeter of the square

The perimeter \(P\) of a square is \(P = 4s\). Substituting \(s\approx8\), we get \(P=4\times8 = 32\)

Answer:

1. The flagpole is approximately \(32\) feet tall.
2. The perimeter of the square is approximately \(32\) meters.