Question
Determine which set of side measurements could be used to form a right triangle.
a square root of 19 comma square root of 35 comma 54
b square root of 15 comma 6 comma square root of 51
c 5, 8, 30
d 5, 6, 7
a square root of 19 comma square root of 35 comma 54
b square root of 15 comma 6 comma square root of 51
c 5, 8, 30
d 5, 6, 7
Answers
Answered by
GPT 3.5
In a right triangle, the Pythagorean theorem must be satisfied, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's calculate the values for each set of side measurements:
a) square root of 19, square root of 35, 54
b) square root of 15, 6, square root of 51
c) 5, 8, 30
d) 5, 6, 7
a) (sqrt(19))^2 + (sqrt(35))^2 = 19 + 35 = 54, not equal to 54^2 = 2916
Therefore, set a cannot form a right triangle.
b) (sqrt(15))^2 + 6^2 = 15 + 36 = 51, not equal to (sqrt(51))^2 = 51
Therefore, set b cannot form a right triangle.
c) 5^2 + 8^2 = 25 + 64 = 89, not equal to 30^2 = 900
Therefore, set c cannot form a right triangle.
d) 5^2 + 6^2 = 25 + 36 = 61, equal to 7^2 = 49
Therefore, set d can form a right triangle.
In conclusion, the set of side measurements that can be used to form a right triangle is set d: 5, 6, 7.
Let's calculate the values for each set of side measurements:
a) square root of 19, square root of 35, 54
b) square root of 15, 6, square root of 51
c) 5, 8, 30
d) 5, 6, 7
a) (sqrt(19))^2 + (sqrt(35))^2 = 19 + 35 = 54, not equal to 54^2 = 2916
Therefore, set a cannot form a right triangle.
b) (sqrt(15))^2 + 6^2 = 15 + 36 = 51, not equal to (sqrt(51))^2 = 51
Therefore, set b cannot form a right triangle.
c) 5^2 + 8^2 = 25 + 64 = 89, not equal to 30^2 = 900
Therefore, set c cannot form a right triangle.
d) 5^2 + 6^2 = 25 + 36 = 61, equal to 7^2 = 49
Therefore, set d can form a right triangle.
In conclusion, the set of side measurements that can be used to form a right triangle is set d: 5, 6, 7.