Question

Rounded to the nearest tenth, what is the perimeter of the triangle? a 30-60-90 triangle with a hypotenuse of length of 5 cm A. 9.3 centimeters B. 10.8 centimeters C. 11.0 centimeters D. 11.8 centimeters E. 16.2 centimeters

Answer 1

the correct answer is D. 11.8 centimeters.

Step-by-step explanation:

The shorter leg would be half the length of the hypotenuse, which is 5/2 = 2.5 cm.

The longer leg would be √3 times the length of the shorter leg, which is √3 * 2.5 ≈ 4.33 cm (rounded to the nearest hundredth).

To find the perimeter, we add up the lengths of all three sides:

5 cm + 2.5 cm + 4.33 cm = 11.83 cm (rounded to the nearest hundredth).

Therefore, rounded to the nearest tenth, the perimeter of the triangle is 11.8 centimeters.

Answer 2

The perimeter of a 30-60-90 triangle with a hypotenuse of 5 cm is calculated using the ratios specific to this type of triangle. The perimeter is the sum of all three sides, resulting in D)11.8 cm when rounded to the nearest tenth.

Step-by-step explanation:

The question asks for the perimeter of a 30-60-90 triangle with a hypotenuse of length 5 cm, rounded to the nearest tenth. In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. Therefore, if the hypotenuse is 5 cm, the shorter leg (opposite the 30-degree angle) is half the hypotenuse, which is 2.5 cm, and the longer leg (opposite the 60-degree angle) is the shorter leg times √3, which is approximately 4.33 cm. To find the perimeter, we add up the lengths of all three sides.

Perimeter = shorter leg + longer leg + hypotenuse
= 2.5 cm + 4.33 cm + 5 cm
= 11.8 cm

Thus, the perimeter of the triangle rounded to the nearest tenth is 11.8 centimeters, which corresponds to option D.