Question

1.Are 24, 45, and 51 the side measurements of a special right triangle?

Answer 1

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45–45–90. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods.

Now you decide whether it is special right triangle?

Answer 2

Source
http://en.wikipedia.org/wiki/Special_right_triangles

Answer 3

they arent?

Answer 4

They are measurements of special right triangle
Reason:

the measurements of any right triangle, If they are, then Pythagoras's Theorem must apply; the square of the longest side is equal to the sum of the squares of the other two sides, in other words
51² = 24² + 45².
But 51² = 2601.
And 24² + 45² = 576 + 2025 = 2601, so yea they are the side measurements of a special right triangle.