Find the perimeter of a 30°-60°-90° triangle whose shorter leg is 16cm

the ratio of sides of your triangle are

1:√3:2 or x : √3x : 2x

given x = 16
other sides are 16√3 and 32
perimeter = .... just add them up

To find the perimeter of a 30°-60°-90° triangle, we need to know the lengths of all three sides.

In a 30°-60°-90° triangle, the ratio of the lengths of the sides is:

Shorter leg : Longer leg : Hypotenuse = 1 : √3 : 2

Given that the shorter leg is 16 cm, we can use this ratio to find the lengths of the other two sides.

Shorter leg = 16 cm
Longer leg = (√3) * shorter leg = (√3) * 16 cm = 16√3 cm
Hypotenuse = 2 * shorter leg = 2 * 16 cm = 32 cm

Now, we can calculate the perimeter of the triangle by adding the lengths of all three sides together:

Perimeter = Shorter leg + Longer leg + Hypotenuse
= 16 cm + 16√3 cm + 32 cm

Therefore, the perimeter of the 30°-60°-90° triangle with a shorter leg of 16 cm is 16 cm + 16√3 cm + 32 cm.

To find the perimeter of a 30°-60°-90° triangle, we need to know the lengths of the three sides: the shorter leg (opposite the 30° angle), the longer leg (opposite the 60° angle), and the hypotenuse (opposite the 90° angle).

In a 30°-60°-90° triangle, the shorter leg is half the length of the hypotenuse, and the longer leg is √3 times the length of the shorter leg.

Given that the length of the shorter leg is 16 cm, we can calculate the lengths of the other sides as follows:

- The longer leg: 16 cm × √3 = 16√3 cm
- The hypotenuse: 2 × 16 cm = 32 cm

Now, we can find the perimeter by adding the lengths of all three sides:

Perimeter = shorter leg + longer leg + hypotenuse
= 16 cm + 16√3 cm + 32 cm

Since the second and third terms are not like terms, we cannot simplify it further.

Therefore, the perimeter of the 30°-60°-90° triangle is 16 cm + 16√3 cm + 32 cm.