Question

Which of the following are not the lengths of the sides of a 30°-60°-90° triangle?

A. 1/2, √3/2, 1
B. 5/2, 5√3/2, 10
C. √2, √6,2√2
D. 3,3√3,6

Answer 1

C

Explanation:

C. √2, √6,2√2 are not the lengths of the sides of a 30°-60°-90° triangle.

In a 30°-60°-90° triangle the ratio of the sides are always the same, the hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg.

A. 1/2, √3/2, 1 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 1, the longer leg is 1√3=√3 and the hypotenuse is 12=2.

B. 5/2, 5√3/2, 10 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 5/2, the longer leg is (5/2)*√3=5√3/2 and the hypotenuse is (5/2)*2=5

D. 3,3√3,6 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 3, the longer leg is 3√3=3√3 and the hypotenuse is 32=6

So, option C is not the lengths of a 30°-60°-90° triangle.