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given : △abc (to the right), ab = 15, bd = 9,
ad ⊥bc m∠c = 30°. find the perimeter of triangle.

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

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1

step-by-step explanation: