The length of the hypotenuse of a 30-60-90 triangle is 18. what is the perimeter?

i have no idea how to start this or how to do this.

The answer is 27 + 9√3.

Let c be a hypotenuse of a triangle and a and b two legs.

c = 18

In a 30°-60°-90° triangle, the hypotenuse (c) is twice the length of the shorter leg (a):
c = 2a   ⇒ a =  c ÷ 2 = 18 ÷ 2 = 9

In a 30°-60°-90° triangle, the longer leg is equal to the shorter leg multiplied by √3:
b = √3a = √3 · 9 = 9√3

Now we have the length of all three sides:
a = 9
b = 9√3 = √6² · √3 = √36 · √3 = √(36 · 3) = √108
c = 18

So, the perimeter (P) of the triangle is:
P = a + b + c = 9 + 9√3 + 18 = 27 + 9√3

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for