Geometry B Semester Exam help please
i am on 13 right now
13. The length of the hypotenuse of a 30 -60 -90 triangle is 11 what is the perimeter
a 11/2 +33/2 divide 3
b 33/2+11/2 divide 3
c 11+33 divide 3
d 33+11 divide 3
please help
the sides are in the ratio 1:√3:2
so if the hypotenuse is 11, the sides are
11/2, 11/2 √3, 11
That makes the perimeter 11/2 (3+√3)
I think you mangles your choices, since you need a √3 somewhere in there.
To find the perimeter of a triangle, you need to add up the lengths of all three sides.
In the given question, we have a 30-60-90 triangle, which is a special right triangle with specific angle measurements and side ratios. In a 30-60-90 triangle, the shorter leg is half the length of the hypotenuse, and the longer leg is √3 times the length of the shorter leg.
Given that the length of the hypotenuse is 11, we can find the lengths of the other two sides using the side ratios.
The length of the shorter leg is half the length of the hypotenuse: 11/2 = 5.5.
The length of the longer leg is √3 times the length of the shorter leg: √3 * 5.5 = 5.5√3.
Now, to find the perimeter, we add up the lengths of all three sides:
Perimeter = 11 + 5.5 + 5.5√3.
To simplify the answer, we can try to rationalize the denominator (√3) by multiplying both the numerator and the denominator by √3:
Perimeter = 11 + 5.5 + (5.5√3 * √3)/(√3).
Simplifying further:
Perimeter = 11 + 5.5 + (16.5√3)/√3.
Perimeter = 11 + 5.5 + 16.5.
Perimeter = 33.
So, the correct option for the perimeter is c) 11+33 divided by 3.
Therefore, the answer is c) 11+33 divided by 3.