Question

find the length of the hypotenuse of the right triangle pictured below. question help: video post to forum submit question question 23 a 14 - inch laptop has a screen that is 9 inches tall. how wide is the screen? approximate the width to the nearest hundredth. note: laptops and tv screens are measured based on their diagonal length (corner to corner). question help: video post to forum submit question question 24

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 5\) and \(b = 12\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=5^{2}+12^{2}\).

Step2: Calculate the squares

\(5^{2}=25\) and \(12^{2}=144\). Then \(c^{2}=25 + 144=169\).

Step3: Find the square - root

\(c=\sqrt{169}=13\).

for second question:

Step1: Identify values for Pythagorean theorem

The diagonal of the laptop screen is \(d = 14\) inches (hypotenuse of a right - triangle) and the height \(h = 9\) inches. Let the width be \(w\). By the Pythagorean theorem \(d^{2}=h^{2}+w^{2}\), so \(w^{2}=d^{2}-h^{2}\).

Step2: Substitute values

\(w^{2}=14^{2}-9^{2}=196 - 81=115\).

Step3: Find the square - root

\(w=\sqrt{115}\approx10.72\) inches.

Answer:

13