A triangle has sides of 24in, 45in, 51in. Is the triangle a right triangle?
Yes, the triangle is a right triangle because it satisfies the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have:
24^2 + 45^2 = 576 + 2025 = 2601
51^2 = 2601
Since both sides of the equation are equal, the triangle satisfies the Pythagorean theorem and is therefore a right triangle.
Which of these is a pythagorean triple?
Responses
9, 40, 41
9, 40, 41
7, 26, 89
7, 26, 89
1, 2, 3
1, 2, 3
36, 48, 62
9, 40, 41 is a Pythagorean triple.
Analyse results
Biodiversity Portfolio
Procedure
1. Place all the beans in their own cups
2. The red beans represent sunlight, the white beans water, and the black space
3. The animals will need four or more resource to survive.
4. Dump the beans on the table and pick as many as I can in 1 minute
5. write the results
Materials
3 cups, 10 red beans, 10 white beans, 10 black beans, paper, pencil and a timer
Results
A Table shows
Red beans
(Sunlight)
White beans
(Water)
Black beans
(Space)
Bear has red beans 7 white beans 4 black beans 6
Wolf has red beans 3 White beans 6 black beans 4
Analysis:
The bean experiment simulates biodiversity in an ecosystem. The red beans represent sunlight, the white beans represent water and the black beans represent space. The survival of animals in the ecosystem was tested by picking as many beans as possible within a minute.
The bear and wolf in the experiment needed four or more resources to survive. The bear picked seven red beans for sunlight, four white beans for water, and six black beans for space. The bear was able to find enough resources to survive easily. The wolf picked three red beans for sunlight, six white beans for water, and four black beans for space. The wolf was also able to find enough resources to survive, but it was less successful than the bear as it took fewer red beans for sunlight. This could indicate that the wolf may struggle to find enough food and may have to hunt over larger area than the bear.
Overall, this experiment shows how different animals require different combinations and amounts of resources to survive, and how a lack of resources can limit their survival. It highlights the importance of maintaining biodiversity in ecosystems so that all animals can find the resources they need to survive.
To determine if the triangle is a right triangle, we can apply the Pythagorean theorem. According to the theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.
Let's calculate:
24^2 + 45^2 = 576 + 2025 = 2601
51^2 = 2601
Since 24^2 + 45^2 = 51^2, the triangle satisfies the Pythagorean theorem, which means it is a right triangle.
To determine if a triangle is a right triangle, we can use the Pythagorean Theorem. The Pythagorean 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.
Let's calculate the squares of the given side lengths:
- The square of 24 inches is 576 in².
- The square of 45 inches is 2025 in².
- The square of 51 inches is 2601 in².
Now, we need to check if the sum of the squares of the two shorter sides is equal to the square of the longest side (hypotenuse).
In this case, the sum of the squares of 24 inches and 45 inches is 576 in² + 2025 in² = 2601 in², which is equal to the square of 51 inches.
Since the sum of the squares of the two shorter sides is equal to the square of the longest side, this triangle obeys the Pythagorean Theorem. Therefore, the triangle with side lengths of 24 inches, 45 inches, and 51 inches is indeed a right triangle.