A steel plate is 20 mm thick and 45 mm wide. What is the length of the diagonal across the plate?
49.24 mm
To determine the diagonal of a rectangular steel plate, we will use the Pythagorean theorem. This theorem is applicable since the steel plate can be imagined as a rectangle, and the diagonal forms the hypotenuse of a right-angled triangle, with the plate's width and thickness serving as the perpendicular and base.
The formula for the diagonal \(d\) of a rectangle, where \(w\) is width and \(t\) is thickness, is given by:
\(d = \sqrt{w^2 + t^2}\)
Given:
- Width, \(w = 45 \, \text{mm}\)
- Thickness, \(t = 20 \, \text{mm}\)
Plug the values into the formula:
\(d = \sqrt{45^2 + 20^2}\)
\(d = \sqrt{2025 + 400}\)
\(d = \sqrt{2425}\)
\(d \approx 49.24 \, \text{mm}\)
Hence, the length of the diagonal across the plate is approximately \(49.24 \, \text{mm}\). This matches the third option provided, confirming it as the correct answer.
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