Question

select the correct answer.
rounded to the nearest tenth, what is the perimeter of the triangle?
triangle image with 60°, 30°, right angle, hypotenuse 5 cm
a. 9.3 centimeters
b. 10.8 centimeters
c. 11.0 centimeters
d. 11.8 centimeters
e. 16.2 centimeters

Explanation:

Step1: Identify triangle type

This is a 30-60-90 right triangle, hypotenuse $c=5$ cm.

Step2: Find shorter leg

Shorter leg $a=\frac{1}{2}c$
$a=\frac{1}{2} \times 5 = 2.5$ cm

Step3: Find longer leg

Longer leg $b=a\sqrt{3}$
$b=2.5\sqrt{3} \approx 2.5 \times 1.732 = 4.33$ cm

Step4: Calculate perimeter

Perimeter $P=a+b+c$
$P=2.5 + 4.33 + 5 = 11.83$ cm

Step5: Round to nearest tenth

$P \approx 11.8$ cm

Answer:

D. 11.8 centimeters