The length of the hypotenuse of a 30°−60°−90°30°−60°−90° triangle is 18. What is the perimeter?(1 point) Responses 27+93–√27+9327 plus 9 square root of 3 54+183–√54+18354 plus 18 square root of 3 12+363–√12+36312 plus 36 square root of 3 18+63–√

Answer 1

The perimeter of a triangle is the sum of the lengths of all its sides.

In a 30°−60°−90° triangle, the sides are in the ratio 1:√3:2.

Let x be the length of the shortest side (opposite the 30° angle). Then the length of the hypotenuse (opposite the 90° angle) is 2x.

Since we are given that the hypotenuse is 18, we have:
2x = 18
x = 9

The sides of the triangle are 9, 9√3, and 18.

Therefore, the perimeter is:
9 + 9√3 + 18
= 27 + 9√3

So, the perimeter is 27 + 9√3, which is the second option.