Question
Determine which set of side measurements could be used to form a right triangle.
a 4, 11, 20
b 16, 21, 25
c 5, 13, 25
d 3, 4, 5
a 4, 11, 20
b 16, 21, 25
c 5, 13, 25
d 3, 4, 5
Answers
Answered by
GPT 3.5
To determine which set of side measurements could form a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's try each set of side measurements:
a) Using the theorem, we have 4² + 11² = 16 + 121 = 137, which is not equal to 20² = 400. Therefore, set a cannot form a right triangle.
b) Again using the theorem, we have 16² + 21² = 256 + 441 = 697, which is not equal to 25² = 625. Thus, set b cannot form a right triangle.
c) Again using the theorem, we have 5² + 13² = 25 + 169 = 194, which is not equal to 25² = 625. Therefore, set c cannot form a right triangle.
d) Once again, applying the theorem, we have 3² + 4² = 9 + 16 = 25, which is equal to 5² = 25. Thus, set d can form a right triangle.
Therefore, the answer is set d: 3, 4, and 5.
Let's try each set of side measurements:
a) Using the theorem, we have 4² + 11² = 16 + 121 = 137, which is not equal to 20² = 400. Therefore, set a cannot form a right triangle.
b) Again using the theorem, we have 16² + 21² = 256 + 441 = 697, which is not equal to 25² = 625. Thus, set b cannot form a right triangle.
c) Again using the theorem, we have 5² + 13² = 25 + 169 = 194, which is not equal to 25² = 625. Therefore, set c cannot form a right triangle.
d) Once again, applying the theorem, we have 3² + 4² = 9 + 16 = 25, which is equal to 5² = 25. Thus, set d can form a right triangle.
Therefore, the answer is set d: 3, 4, and 5.