Final answer:
To arrange the right triangles from least to greatest, calculate the length of their unlabeled sides using the Pythagorean theorem and compare them. For example, a triangle with sides 3, 4, and 5 units long will have an unlabeled side of 4 units.
Step-by-step explanation:
To arrange the right triangles from least to greatest, we need to compare the lengths of their unlabeled sides. One way to determine the length of the unlabeled side is to use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For example, let's consider the triangles with sides 3, 4, and 5 units long, and 5, 12, and 13 units long. Using the Pythagorean theorem, we can calculate the length of the unlabeled side in each triangle:
Triangle 1: unlabeled side = √(5^2 - 3^2) = √(25 - 9) = √16 = 4 units
Triangle 2: unlabeled side = √(13^2 - 12^2) = √(169 - 144) = √25 = 5 units
Therefore, the triangles can be arranged in order from least to greatest based on the length of their unlabeled sides:
- Triangle with unlabeled side of 4 units
- Triangle with unlabeled side of 5 units