We can restate the Pythagorean relationship using algebra.
The Pythagorean Theorem
In a right triangle, where \(c\) represents the length of the hypotenuse, and \(a\) and \(b\) represent the lengths of the two legs, the following equation is true:
In an electronics store, two computer monitors are both described to have a \(19\) inch screen, but their rectangular shapes are not congruent.
Retailers list the sizes of computer monitors and televisions as a single number. How are the sizes of computer monitors and televisions determined?
The sizes of monitors and televisions are described by the length of their diagonals.
Monitor 1
Monitor 2
The width of Monitor 1 is \(16.4\) inches and its height is \(9.2\) inches. Monitor 2 has a width of \(15.2\) inches and a height of \(11.4\) inches.
Let \(h\) represent the length of the hypotenuse of Monitor 1, \(h\gt0\).
By the Pythagorean Theorem,
\(h^2\)
\(=(16.4)^2+(9.2)^2\)
\(=268.96+84.64\)
\(= 353.6\)
\(h\)
\(=\sqrt{353.6}= 18.804\ldots\)
Therefore, the diagonal of Monitor 1 has an approximate length of \(18.8\) inches.
Let \(k\) represent the length of the hypotenuse of Monitor 2.
\(k^2\)
\(=(15.2)^2+(11.4)^2\)
\(=234.04+129.96\)
\(= 361\)
\(k\)
\(=\sqrt{361} =19\), since \(k \gt 0\)
Therefore, the diagonal of Monitor 2 has a length of \(19\) inches.
Even though Monitor 1 and Monitor 2 are different shapes, they are both \(19\) inch monitors.