1. Which set represents a Pythagorean triple?
A:2,5,6
B:6,8,10
C:8,8,128
D:8,10,256
2. What is the hypotenuse of a right triangle if the legs are each 20 inches long? Round to the nearest whole number.
A:28
B:29
C:30
D:31
I think the first ones B, and the second one is C
1B is correct
2C is wrong
20*1.414 = 28.28, which rounds to 28, not 29
oh thanks
To determine if a set represents a Pythagorean triple, we need to check if it satisfies 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.
For the first question, let's examine each set:
A: 2, 5, 6
The squares of the sides are: 2^2 = 4, 5^2 = 25, 6^2 = 36
Now, check if the sum of the squares of the two smaller sides is equal to the square of the longest side:
4 + 25 = 29
Since 29 is not equal to 36, this set does not satisfy the Pythagorean theorem.
B: 6, 8, 10
The squares of the sides are: 6^2 = 36, 8^2 = 64, 10^2 = 100
Sum of the squares of the two smaller sides: 36 + 64 = 100
The sum is equal to the square of the longest side.
Therefore, this set (6, 8, 10) represents a Pythagorean triple.
C: 8, 8, 128
The squares of the sides are: 8^2 = 64, 8^2 = 64, 128^2 = 16384
Sum of the squares of the two smaller sides: 64 + 64 = 128
The sum is not equal to the square of the longest side.
Therefore, this set does not represent a Pythagorean triple.
D: 8, 10, 256
The squares of the sides are: 8^2 = 64, 10^2 = 100, 256^2 = 65536
Sum of the squares of the two smaller sides: 64 + 100 = 164
The sum is not equal to the square of the longest side.
Therefore, this set does not represent a Pythagorean triple.
Based on this analysis, you are correct. The set that represents a Pythagorean triple is B: 6, 8, 10.
Now, moving on to the second question about finding the hypotenuse of a right triangle with legs of 20 inches each. To find the length of the hypotenuse, we can apply the Pythagorean theorem.
Let's denote the legs of the right triangle as leg A and leg B, and the hypotenuse as C.
Using the Pythagorean theorem, we have the equation:
A^2 + B^2 = C^2
Plugging in the values, we get:
20^2 + 20^2 = C^2
400 + 400 = C^2
800 = C^2
To find the value of C, we take the square root of both sides:
C = √800 = 28.28427 (approx)
Since we need to round the answer to the nearest whole number, the correct answer is A: 28.
Therefore, your answer for the second question is incorrect. The hypotenuse of a right triangle with legs of 20 inches each is approximately 28, rounded to the nearest whole number.