SOLUTION: What is the perimeter of a 30-60-90 triangle with an altitude of 12?

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Question 682416: What is the perimeter of a 30-60-90 triangle with an altitude of 12?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Theorem. In a 30°-60°-90° triangle the sides are in the ratio 1+%3A+2+%3A+sqrt%283%29
sketch this triangle and mark the smallest side b with length +1, the longer side with a +sqrt%283%29, and hypotenuse c with 2
then sketch another similar 30°-60°-90° triangle and mark the smallest side b with length +b=12, the longer side with +a, and hypotenuse AB with c

use ratio to find sides:
b%3Aa=1%3Asqrt%283%29..........plug in +b=12
12%3Aa=1%3Asqrt%283%29.......solve for a
a=12sqrt%283%29
a=12%2A1.7320508075688772935274463415059
a=20.785

b%3Ac=1%3A2
12%3Ac=1%3A2
c=24

so,the perimeter of a 30-60-90 triangle with an altitude of 12 will be:
P=a%2Bb%2Bc
P=20.785%2B12%2B24
P=56.785