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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.

Verified Answer :

JcAlmighty

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:27 + 9 qrt 3

Step-by-step explanation:

because ^ dude said it and i need points

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