Question

1. modeling real life television sizes are measured by the lengths of their diagonals. you want to purchase a television that is at least 40 inches. should you purchase the television shown? explain your reasoning. 36 in. 20.25 in.

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 20.25\) and \(b=36\). The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the diagonal.
So \(c^{2}=(20.25)^{2}+36^{2}\)
\(c^{2}=410.0625 + 1296\)
\(c^{2}=1706.0625\)

Step2: Solve for \(c\)

Take the square - root of \(c^{2}\). \(c=\sqrt{1706.0625}\)
\(c = 41.3\) (rounded to one decimal place)

Answer:

Since \(41.3>40\), you should purchase the television.