Let's solve for the diagonal length of a square floppy diskette that measures 5 inches on each side.
1. Understand the Problem:
- We have a square with each side measuring 5 inches.
- We need to find the diagonal length of this square.
2. Formulate the Mathematical Approach:
- The diagonal of a square can be calculated using the Pythagorean theorem.
- For a square, the diagonal splits the square into two right-angled triangles.
- Each leg of the triangle, corresponding to the sides of the square, is 5 inches.
- The diagonal is the hypotenuse of these triangles.
3. Apply the Pythagorean Theorem:
[tex]\[
\text{diagonal}^2 = \text{side}^2 + \text{side}^2
\][/tex]
Substituting 5 inches for the sides:
[tex]\[
\text{diagonal}^2 = 5^2 + 5^2
\][/tex]
4. Calculate the Values:
[tex]\[
5^2 = 25
\][/tex]
Thus,
[tex]\[
\text{diagonal}^2 = 25 + 25 = 50
\][/tex]
5. Solve for the Diagonal:
- Taking the square root of both sides:
[tex]\[
\text{diagonal} = \sqrt{50}
\][/tex]
6. Simplify the Solution:
- The diagonal length of the square floppy diskette is [tex]\(\sqrt{50}\)[/tex] inches.
Given the choices:
A) [tex]\(\sqrt{50}\)[/tex] in.
B) [tex]\(\sqrt{55}\)[/tex] in.
C) [tex]\(\sqrt{51}\)[/tex] in.
D) [tex]\(\sqrt{58}\)[/tex] in.
The correct answer is:
A) [tex]\(\sqrt{50}\)[/tex] in.
Additionally, converting [tex]\(\sqrt{50}\)[/tex] to a decimal gives approximately 7.071 inches.
Therefore, the diagonal length of the diskette is approximately 7.071 inches, and the correct multiple-choice answer is A) [tex]\(\sqrt{50}\)[/tex] in.
