Question

The length of the hypotenuse of a 30-60-90 triangle is 4. Find the perimeter. Round to the nearest tenth if necessary.

a. 8.0
b. 10.4
c. 11.0
d. 12.0

Answer 1

The perimeter of the 30-60-90 triangle is approximately 10.4.

Step-by-step explanation:

To find the perimeter of a 30-60-90 triangle with a hypotenuse of 4, we need to find the lengths of the other two sides of the triangle.

In a 30-60-90 triangle, the side opposite the 30-degree angle (short leg) is half the length of the hypotenuse, and the side opposite the 60-degree angle (long leg) is √3 times the length of the short leg.

Therefore, the short leg is 4/2 = 2 units and the long leg is 2√3 units.

The perimeter of the triangle is the sum of all three sides.

So, the perimeter = hypotenuse + short leg + long leg = 4 + 2 + 2√3 = 6 + 2√3. Rounding to the nearest tenth, the perimeter is approximately 10.4.