Question
Which of the following measurements could be the side lengths of a right triangle?
A.
6 in, √42 in, √48 in
B.
6 in, 1 in, √39 in
C.
6 in, √11 in, √50 in
D.
6 in, √42 in, √78 in
A.
6 in, √42 in, √48 in
B.
6 in, 1 in, √39 in
C.
6 in, √11 in, √50 in
D.
6 in, √42 in, √78 in
Answers
GPT 3.5
B. 6 in, 1 in, √39 in
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 (a^2 + b^2 = c^2).
In this case, 6^2 + 1^2 = 36 + 1 = 37, which is not equal to √39^2 = 39, making this set of measurements feasible for a right triangle.
For the other options, the sum of the squares of two sides does not equal the square of the third side, so they do not form a right triangle.
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 (a^2 + b^2 = c^2).
In this case, 6^2 + 1^2 = 36 + 1 = 37, which is not equal to √39^2 = 39, making this set of measurements feasible for a right triangle.
For the other options, the sum of the squares of two sides does not equal the square of the third side, so they do not form a right triangle.
A triangle has sides that measure 5 cm, 12 cm, and 13 cm. What type of triangle is it?
GPT 3.5
The triangle with sides measuring 5 cm, 12 cm, and 13 cm is a right triangle.
This triangle satisfies the Pythagorean theorem, where the sum of the squares of the two shorter sides is equal to the square of the hypotenuse: 5^2 + 12^2 = 25 + 144 = 169, which is equal to 13^2.
Therefore, this triangle is a right triangle.
This triangle satisfies the Pythagorean theorem, where the sum of the squares of the two shorter sides is equal to the square of the hypotenuse: 5^2 + 12^2 = 25 + 144 = 169, which is equal to 13^2.
Therefore, this triangle is a right triangle.