SOLUTION: Quick Check in Special Right Triangles: 5. An equilateral triangle has an altitude of 15 m. What is the perimeter of that triangle? A) 30 square root 2 m B) 45 m C) 30 square r

Algebra ->  Triangles -> SOLUTION: Quick Check in Special Right Triangles: 5. An equilateral triangle has an altitude of 15 m. What is the perimeter of that triangle? A) 30 square root 2 m B) 45 m C) 30 square r      Log On


   

Question 1114865: Quick Check in Special Right Triangles:
5. An equilateral triangle has an altitude of 15 m. What is the perimeter of that triangle?
A) 30 square root 2 m
B) 45 m
C) 30 square root 3 m
D) 60 square root 3 m
Found 2 solutions by math_helper, josgarithmetic:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
One way the side can be found is by sin(60) = 15/s —> +s+=+10%2Asqrt%283%29+ m
The perimeter is 3 times that: +highlight%28++30%2Asqrt%283%29+%29+ m

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
The altitude cuts the equilateral triangle into two congruent special 30-60-90 right triangles, each with legs x and hypotenuse 2x:

The 2x would be ONE side of the equilateral triangle.

15%5E2%2Bx%5E2=4x%5E2
15%5E2=3x%5E2
3%2A5%2A15=3%2Ax%5E2
5%2A15=x%5E2
x=sqrt%285%2A5%2A3%29
x=5%2Asqrt%283%29
-
Perimeter of equilateral triangle:
3%2A2%2A5%2Asqrt%283%29
30%2Asqrt%283%29