To find the perimeter of a 30-60-90 degree triangle, we need to know the lengths of the sides. A 30-60-90 triangle is a special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees, and the sides are in a particular ratio.
In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:β3:2. The shorter leg is the side opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is opposite the 90-degree angle.
In this case, the shorter leg is 16 cm. To find the lengths of the other sides, we can use the ratio of 1:β3:2.
Shorter leg = 1x
Longer leg = β3x
Hypotenuse = 2x
Now, we can solve for x by setting up an equation using the lengths of the sides:
1x = 16 cm
Dividing both sides of the equation by 1, we find that x = 16 cm.
Now we can find the lengths of the other sides:
Longer leg = β3x = β3 * 16 cm β 27.71 cm
Hypotenuse = 2x = 2 * 16 cm = 32 cm
Finally, we can calculate the perimeter by adding the lengths of all three sides:
Perimeter = Shorter leg + Longer leg + Hypotenuse
Perimeter = 16 cm + 27.71 cm + 32 cm
Perimeter β 75.71 cm
So, the perimeter of the 30-60-90 triangle with a shorter leg of 16 cm is approximately 75.71 cm.