Approved Tutor Answer1 Year agoTo determine which of the given lengths can be the sides of a right triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we need to check combinations of the provided lengths: 2.5 cm, 6.5 cm, 6.5 cm, and 6 cm.
We have four lengths to consider: 2.5 cm, 6.5 cm, 6.5 cm, and 6 cm. To form a right triangle, we will check different combinations of these lengths to see if they satisfy the Pythagorean theorem.
Now, applying the Pythagorean theorem:
(Hypotenuse)^2 = (Side 1)^2 + (Side 2)^2
6.5^2 = 2.5^2 + 6^2
Calculating each term:
Now, adding the squares of the two shorter sides:
6.25 + 36 = 42.25
Since both sides of the equation are equal, this combination can indeed form a right triangle.
Applying the Pythagorean theorem again:
6.5^2 = 6.5^2 + 6^2
Calculating:
Now, adding the squares of the two shorter sides:
42.25 ≠ 36
This combination does not satisfy the Pythagorean theorem, so it cannot form a right triangle.
We already checked this combination in the first example, and it works. Thus, it can form a right triangle.
From our analysis, the only combination that can form a right triangle is 2.5 cm, 6 cm, and 6.5 cm. The other combinations do not satisfy the Pythagorean theorem. When working with triangles, especially right triangles, always remember to identify the longest side as the hypotenuse and apply the theorem accordingly. This method will help you determine the validity of any triangle's side lengths effectively.
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