Question

laptop computers are measured according to the diagonals of their screens. a(n) 19-inch laptop has a screen that is 7 inches tall. how wide is the screen? round your approximation to 2 decimal places. approximate answer: inches

Explanation:

Step1: Identify the formula

The laptop screen is a rectangle, so we can use the Pythagorean theorem. For a right triangle with legs \(a\) (height), \(b\) (width), and hypotenuse \(c\) (diagonal), the formula is \(a^{2}+b^{2}=c^{2}\). We know \(a = 7\) and \(c = 19\), so we solve for \(b\): \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 7\) and \(c = 19\) into the formula: \(b=\sqrt{19^{2}-7^{2}}\). First, calculate \(19^{2}=361\) and \(7^{2}=49\). Then, \(19^{2}-7^{2}=361 - 49=312\). So, \(b=\sqrt{312}\).

Step3: Calculate the square root

Calculate \(\sqrt{312}\approx17.66\) (rounded to two decimal places).

Answer:

\(17.66\)