Question

the size of a rectangular computer monitor is determined by the length of its diagonal. if a computer monitor has a length of 24 inches and a height of 18 inches, what is the length of its diagonal to the nearest inch? 42 inches 30 inches 21 inches 15 inches

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the length and height of the rectangle (monitor) are the legs of a right triangle, and the diagonal is the hypotenuse. We can use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c = \sqrt{a^2 + b^2}\). Here, \(a = 24\) inches and \(b = 18\) inches.

Step2: Apply the Pythagorean theorem

First, calculate \(a^2\) and \(b^2\):
\(a^2 = 24^2 = 576\)
\(b^2 = 18^2 = 324\)

Then, find the sum of these squares:
\(a^2 + b^2 = 576 + 324 = 900\)

Now, take the square root of the sum to find the length of the diagonal \(c\):
\(c = \sqrt{900} = 30\)

Answer:

30 inches