Question

1. choose the correct answer.

tanya wants to buy a flat screen television that will just fit into the space in her entertainment center. the dimensions of the opening where the television would sit are width equal to 37 inches and height equal to 21 inches. knowing that television sizes are named by the measure of the screens diagonal, what is the biggest size television she can get that will fit?
42 inches
58 inches
37 inches
21 inches

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 21\) (height), \(b = 37\) (width), and \(c\) is the diagonal.
So, \(c=\sqrt{21^{2}+37^{2}}\)

Step2: Calculate \(21^{2}\) and \(37^{2}\)

\(21^{2}=441\), \(37^{2}=1369\)
Then \(21^{2}+37^{2}=441 + 1369=1810\)

Step3: Find the square - root

\(c=\sqrt{1810}\approx42.54\)

Answer:

42 inches