Answer:
48 + 12√3 units
Step-by-step explanation:
ALL LENGTHS MUST BE POSITIVE (I did this to avoid writing ± and showing that only + works)
1. Find AD (you'll find why later): 15² = 9² + AD² --> AD² = 144 --> AD = 12
2. 30-60-90: 12-DC-AC --> AC = 24, DC = 12√3 (side opposite of 90 is double side opposite of 30, side opposite of 60 is √3 times the opposite of 30)
P = AB + BD + DC + AC = 15 + 9 + 12√3 + 24 = 48 + 12√3 units
The perimeter of the given triangle ABC will be 59 units.
The space covered by the triangle in the two-dimensional plane will be the area of the triangle. The sum of all the sides of the triangle is called the perimeter of the triangle.
The perimeter of the triangle will be calculated as:-
First, we will calculate the perpendicular AD by using the Pythagorean theorem:-
AD = √( 15² - 9² )
AD = √144
AD = 12 units
Now we will calculate the Side AC by angle property:-
Sin 30 = 12 / AC
AC = 12 / Sin 30
AC = 12 / 0.5 = 26
The perimeter will be the sum of the all the sides of the triangle:-
P = AB + BC + AC
P = 15 + 18 + 26
P = 59 units.
Therefore the perimeter of the given triangle ABC will be 59 units.
To know more about the perimeter of a triangle follow
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