Question
The length of the hypotenuse of a 30°-60°-90° triangle is 16. What is the perimeter?
(1 point)
A. 64+8 √3
B.24+8 √3
C. 16+64 √3
D. 8+24 √3
I think B is the answer but I don’t know, could you check for me?
(1 point)
A. 64+8 √3
B.24+8 √3
C. 16+64 √3
D. 8+24 √3
I think B is the answer but I don’t know, could you check for me?
Answers
GPT 3.5
Yes, you are correct. The answer is B. 24+8√3.
To find the perimeter of the triangle, we need to first find the side lengths. In a 30°-60°-90° triangle, the sides are in the ratio 1:√3:2.
So, if the length of the hypotenuse (which is opposite the 90° angle) is 16, then the shorter leg (opposite the 30° angle) would be 8, and the longer leg (opposite the 60° angle) would be 8√3.
The perimeter of a triangle is the sum of all three sides. Therefore, the perimeter would be 8 + 8√3 + 16 = 24 + 8√3, which matches option B.
To find the perimeter of the triangle, we need to first find the side lengths. In a 30°-60°-90° triangle, the sides are in the ratio 1:√3:2.
So, if the length of the hypotenuse (which is opposite the 90° angle) is 16, then the shorter leg (opposite the 30° angle) would be 8, and the longer leg (opposite the 60° angle) would be 8√3.
The perimeter of a triangle is the sum of all three sides. Therefore, the perimeter would be 8 + 8√3 + 16 = 24 + 8√3, which matches option B.