If the area of triangle ABC is 27

Here are a couple of approaches   (EP's is WAY better than mine  !!!  )

https://web2.0calc.com/questions/if-the-area-of-triangle-abc-is-27-what-is-the-value-of-p

Sides: a = 15   b = 3.606   c = 15.62

Area: T = 27
Perimeter: p = 34.226
Semiperimeter: s = 17.113

Angle ∠ A = α = 73.503° = 73°30'12″ = 1.283 rad
Angle ∠ B = β = 13.325° = 13°19'30″ = 0.233 rad
Angle ∠ C = γ = 93.172° = 93°10'18″ = 1.626 rad

Height: ha = 3.6
Height: hb = 14.977
Height: hc = 3.457

Median: ma = 8.5
Median: mb = 15.207
Median: mc = 7.616

If the area of triangle ABC is 27, what is the value of p?

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Solving this geometry problem in several easy steps:

1)   AB = sqrt(12² + 10²) = 15.62049935

2)   CY = 2*27 / AB = 3.456995759

3)   ∠ABO ≅ ∠ YCZ = arctan(12 / 10) = 50.19442891º

4)   OZ = 12 * tan∠ABO = 14.4

5)   CZ = CY / cos∠YCZ = 5.4

6)   p = OZ - CZ = 9

Question: If the area of triangle ABC is 27, what is the value of p?

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In my above post, I was using the wrong diagram. 

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Answer:      A (3, 12)         B (12, 0)           C (0, p)

1/   AB = arctan(12 / 9) = 15

2/   CY = 2*27 / 15 = 3.6

3/    ∠ABO  ≅  ∠YCZ = arctan(12 / 9) = 53.13010235º

4/   OZ = 12 * tan ∠ABO = 16

5/   CZ = CY / cos∠YCZ = 6

6/   p = OZ - CZ = 10

( See above diagram )