Answer:
B.
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : sqrt(3) : 2
From the 1 and 2, we see that the hypotenuse must be twice the length of the short leg.
From the 1 and sqrt(3) we see that the long leg is sqrt(3) times the length of the short leg.
Now we check for these two ratios in each choice.
A.
1 is twice 1/2. Check
sqrt(3)/2 is sqrt(3) times 2. Check
B.
10 is twice 5, not twice 5/2. This does not check.
C.
2sqrt(2) is twice sqrt(2). Check
sqrt(6) is 2sqrt(2) time sqrt(3). Check
D.
6 is twice 3. Check
3sqrt(3) is sqrt(3) times 3. Check
Answer: B.
You just have to add the numbers up.
So the perimeter is 47 ft.
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