Which of the following are measurements of the sides of a right triangle?
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A. 10, 8, 6
B. 13, 12, 5
C. 26, 24, 10
D. all of the above
a^2 + b^2 = c^2
A.
6^2 + 8^2 = 10^2
36 + 64 = 100
Right!
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Try all of the answers using the Pythagorean Theorem.
IDK HOW TO DO THAT
To determine which of the given options are measurements of the sides of a right triangle, we need to apply the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
Let's calculate the squares of the given side measurements:
Option A:
10^2 + 8^2 = 100 + 64 = 164
6^2 = 36
Option B:
13^2 = 169
12^2 + 5^2 = 144 + 25 = 169
Option C:
26^2 = 676
24^2 + 10^2 = 576 + 100 = 676
Now, we have to check if the sum of the squares of the two shorter sides is equal to the square of the longest side for each option.
Option A:
The sum of the squares of the two shorter sides is not equal to the square of the longest side. Thus, option A is not a right triangle.
Option B:
The sum of the squares of the two shorter sides is equal to the square of the longest side. Thus, option B is a right triangle.
Option C:
The sum of the squares of the two shorter sides is equal to the square of the longest side. Thus, option C is a right triangle.
Based on our calculations, options B and C are measurements of the sides of a right triangle. Therefore, the answer is D.