Question

Suppose triangles P, Q, and R have sides with the given measurements.

triangle P: 12, 24, and 30
triangle Q: 9, 40, and 41
triangle R: 5, 18, and 21
Which triangle is a right triangle? Explain your reasoning.














Suppose triangles P, Q, and R have sides with the given measurements.

triangle P: 12, 24, and 30
triangle Q: 9, 40, and 41
triangle R: 5, 18, and 21
Which triangle is a right triangle? Explain your reasoning.










Suppose triangles P, Q, and R have sides with the given measurements.

triangle P: 12, 24, and 30
triangle Q: 9, 40, and 41
triangle R: 5, 18, and 21
Which triangle is a right triangle? Explain your reasoning.


Suppose triangles P, Q, and R have sides with the given measurements.

triangle P: 12, 24, and 30
triangle Q: 9, 40, and 41
triangle R: 5, 18, and 21
Which triangle is a right triangle? Explain your reasoning.


Suppose triangles P, Q, and R have sides with the given measurements.

triangle P: 12, 24, and 30
triangle Q: 9, 40, and 41
triangle R: 5, 18, and 21
Which triangle is a right triangle? Explain your reasoning.

Answer 1

Triangle Q

Explanation:

To know if a triangle is a right triangle given all 3 side lengths, we can use pythagorean theorem, which states:

`a^(2) +b^(2) =c^(2)`

Triangle P: 12,24,30

`12^(2) +24^(2) =30^(2) \\144+576=900\\720 = 900`

FALSE

Triangle Q: 9, 40, 41

`9^(2) +40^(2) =41^(2) \\81+1,600=1,681\\1,681=1,681\\`

TRUE

Triangle R: 5,18,21

`5^(2) +18^(2) =21^(2) \\25+324=441\\349=441`

FALSE

So, Triangle Q is a right triangle.

Hope this helps! :)

Answer 2

A triangle is a right triangle if and only if the sum of the squares of the two shorter sides is equal to the square of the longest side. This is known as the Pythagorean theorem.

Let's check each triangle to see if it satisfies this condition:

Triangle P:

Shortest side = 12

Middle side = 24

Longest side = 30

12^2 + 24^2 = 144 + 576 = 720

30^2 = 900

720 is not equal to 900, so triangle P is not a right triangle.

Triangle Q:

Shortest side = 9

Middle side = 40

Longest side = 41

9^2 + 40^2 = 81 + 1600 = 1681

41^2 = 1681

1681 is equal to 1681, so triangle Q is a right triangle.

Triangle R:

Shortest side = 5

Middle side = 18

Longest side = 21

5^2 + 18^2 = 25 + 324 = 349

21^2 = 441

349 is not equal to 441, so triangle R is not a right triangle.

Therefore, only triangle Q is a right triangle.