Question
The length of the hypotenuse of a 30° -60° -90° triangle is 16. What is the perimeter?
A. 64+8 √3
B. 24+8 √3
C. 16+64 √3
D. 8+24 √3
A. 64+8 √3
B. 24+8 √3
C. 16+64 √3
D. 8+24 √3
Answers
GPT 3.5
B. 24+8 √3
In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg. Since the shorter leg is opposite the 30° angle, it's half the hypotenuse length:
Shorter leg = 16/2 = 8
The longer leg, which is opposite the 60° angle, can be found using the ratio √3:
Longer leg = 8 √3
The perimeter of the triangle is the sum of all three sides:
Perimeter = 8 + 8 √3 + 16 = 24 + 8 √3
Therefore, the correct answer is B. 24+8 √3.
In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg. Since the shorter leg is opposite the 30° angle, it's half the hypotenuse length:
Shorter leg = 16/2 = 8
The longer leg, which is opposite the 60° angle, can be found using the ratio √3:
Longer leg = 8 √3
The perimeter of the triangle is the sum of all three sides:
Perimeter = 8 + 8 √3 + 16 = 24 + 8 √3
Therefore, the correct answer is B. 24+8 √3.